Pith. sign in

REVIEW 3 major objections 4 minor 228 references

Tripartite entanglement: Foundations and applications

T0 review · 3 major / 4 minor · reviewed 2026-08-14 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read Three-qubit entanglement is organised by the GHZ/W class split, and this review follows it from foundations to applications.

desk verdict Wide survey with a still-broken worked teleportation example; fix the erratum and the fidelity derivation before trusting it as a tutorial. read the letter →

arxiv 1909.00862 v2 pith:GLW5M4CI submitted 2019-09-02 quant-ph

Márcio M. Cunha , Alejandro Fonseca , Edilberto O. Silva This is my paper · ORCID
classification quant-ph MSC 81P4081P4581P68 PACS 03.67.Mn03.65.Ud
keywords tripartiteentanglementGHZstatesWquantumnonlocalityteleportationsecretsharingdetectioncontinuousvariables
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This is a review article whose central claim is that tripartite entanglement — entanglement shared by three parties — can be organised around two genuinely different kinds of state, the GHZ class and the W class, and that this distinction carries through from foundational tests of quantum theory to practical quantum information protocols. The paper surveys the foundational side: GHZ states produce a contradiction with local realism without needing a Bell inequality, while W states retain residual bipartite entanglement after tracing out one party. It then walks through applications, including teleportation, dense coding, secret sharing, remote state preparation, continuous-variable settings, and the effect of noise. A sympathetic reader can take the paper as a dependable overview and tutorial, provided the corrected worked examples are internally sound.

What carries the argument

The organising object is the SLOCC classification of pure three-qubit states, which separates genuine tripartite entanglement into two irreducible families: the GHZ state $|\mathrm{GHZ}\rangle = (|000\rangle+|111\rangle)/\sqrt{2}$ and the W state $|W\rangle = (|001\rangle+|010\rangle+|100\rangle)/\sqrt{3}$. These families are inequivalent under stochastic local operations and classical communication: neither can be converted into the other, even probabilistically. The paper uses this dichotomy as a lens through which to organise nonlocality tests, teleportation channels, dense coding, secret sharing, remote preparation, and noise analysis. A second carrying element is the GHZ measurement basis and the EPR/GHZ projection formalism, which supplies the explicit calculations for the teleportation protocols. The erratum attached to the review corrects the earlier version's Section V.A derivation.

What would settle it

Recompute the corrected Section V.A teleportation protocol with a maximally entangled GHZ channel: if the average fidelity expression following Eq. (75) does not evaluate to 1, or if the erratum's basis expansion still refers to an undefined state $|x_2\rangle$, then the worked tutorial is not yet self-consistent.

Watch

Extended reading notes

Core claim

The paper's claim is that the next step beyond two-qubit entanglement — three qubits — already contains a structural richness absent in the bipartite case: under stochastic local operations and classical communication there are exactly two inequivalent classes of genuinely entangled pure states, the GHZ class and the W class. It uses this classification as the backbone of a review of both foundations and applications. On the foundations side, it shows how a GHZ state makes the conflict between quantum mechanics and local realism explicit through a product of three spin measurements, with no inequality required. On the applications side, it reviews and derives teleportation schemes for single-qubit, two-qubit, GHZ, and W states, together with dense coding, quantum cryptography and secret sharing, remote preparation, and continuous-variable analogues. The paper also catalogs experimental production methods, detection witnesses, and the degradation of tripartite entanglement under noise.

Load-bearing premise

The load-bearing premise is that the corrected worked examples of quantum teleportation in Section V.A are mathematically sound, since the paper itself warns that the original calculation was wrong and the erratum still contains unresolved notation.

Editorial extensions

If this is right

  • If the classification claim is right, any three-qubit entanglement resource falls into the GHZ or W class, so protocol performance can be assessed by which class the channel belongs to.
  • If the GHZ nonlocality argument is right, then a single GHZ state is enough to show the conflict between local hidden variables and quantum predictions, without Bell inequalities.
  • If the protocol review is correct, GHZ and W states are usable resources for teleportation, controlled dense coding, quantum secret sharing, and remote state preparation, with W-based teleportation succeeding probabilistically.
  • If the noise analysis is right, tripartite entanglement in realistic settings degrades under decoherence, motivating error-correction and weak-measurement strategies.
  • If the experimental part is right, tripartite GHZ and W states have been produced in multiple platforms, including photons, trapped ions, superconducting qubits, and cavity QED.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Editorial extension: because the paper flags its own Section V.A mistake, a reader should verify every equation in that subsection against the erratum before using it as a teaching resource.
  • Editorial extension: the review stops short of a single side-by-side benchmark of GHZ versus W channels for all protocols; such a table would be a natural next step and is not claimed in the paper.
  • Editorial extension: the GHZ/W split suggests that any future survey of higher-party entanglement could use the same class-first, resource-second organisation, although the paper only sketches those extensions.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. The manuscript is a review of tripartite entanglement. It covers the foundational classification of three-qubit states into GHZ and W classes, Bell nonlocality and the GHZ paradox, a series of quantum information protocols based on tripartite entanglement (teleportation, dense coding, cryptography, remote state preparation), experimental production, detection and characterization, continuous-variable systems, and the influence of noise. The paper's stated aim is to provide a dependable overview and tutorial, and it includes detailed worked calculations for teleportation protocols. A note at the start of Section V.A and an appended erratum indicate that the authors are aware that part of the worked material was incorrect; the erratum is part of the text under review.

Significance. If the manuscript were reliable, it would be a useful entry point to the tripartite-entanglement literature: it assembles a very large bibliography and connects several subfields that are usually treated separately. The descriptive portions on state classification, nonlocality, generation, detection, remote preparation, continuous variables, and noise are broadly consistent with the known physics. The detailed teleportation examples would be pedagogically valuable if they were correct. However, the central tutorial value of the paper is currently compromised by computational errors in the two places where the review actually performs derivations: the EPR-measurement teleportation protocol of Section V.A and the GHZ-measurement teleportation of Section V.B. Because the abstract explicitly promises 'examples of quantum protocols in detail,' these flaws are load-bearing for the paper's main claim rather than cosmetic.

major comments (3)
  1. [Section V.A and Erratum, Eqs. (100)-(101)] The erratum correctly states that original Eq. (41) and Tables I-III are wrong, but the correction is itself inconsistent. Eq. (100) uses an undefined state |x2>_3 and places both terms in the |0>_4 sector. Eq. (101) then uses |x1>_3 and |x2>_3 together with |0>_4 and |1>_4, so the two equations do not agree. Neither equation matches the expansion of Eq. (98) in the basis of Eq. (99), which should read |η00>_34 = |x0>_3(α0 sinθ|0>_4 + α1 cosθ|1>_4) + |x1>_3(α0 cosθ|0>_4 - α1 sinθ|1>_4). As published, the reader cannot tell which formula is normative in the very section that the paper itself flags as mistaken.
  2. [Section V.B, Eqs. (72) and (75)] The averaged-fidelity derivation is internally inconsistent. Eq. (72) states F = |c0|^4 + |c1|^4 + 2 b0 b1 β0 β1 |c0|^2 |c1|^2. Averaging this over the input-state parameters gives ⟨F⟩ = 2/3 + (1/12) sin(2θ) sin(2φ), whereas Eq. (75) reports ⟨F⟩ = 2/3 + (1/3) sin(2θ) sin(2φ). A direct summation of Eq. (71) over the four GHZ outcomes gives the latter expression, so Eq. (72) cannot be an intermediate step on the way to Eq. (75). The factor-of-four discrepancy means the displayed derivation does not support the final formula. In addition, Eq. (73) parameterizes the input as a three-qubit state |Ψ>_in = |c0||000> + |c1|e^{iφ}|111> for a protocol that teleports a single qubit, which makes the calculation impossible to follow as written.
  3. [Section IV, Eqs. (27)-(31)] The GHZ nonlocality argument uses the state |ψ100> from Eq. (13), which for θ=π/4 is (|000> - |111>)/√2. That state is an eigenstate of σx⊗σy⊗σy with eigenvalue +1, not -1 as stated in Eq. (27). The calculation in Eq. (27) writes the state as (|000> + |111>)/√2, which is a different state. Additionally, the text says that σy⊗σx⊗σx yields -1, but the outcome-product algebra in Eq. (30) requires the three correlations σxσyσy, σyσxσy, and σyσyσx. As written, the derivation of the 'Bell's theorem without inequalities' contradiction is not correct and needs to be reconciled with the definitions in Section III.
minor comments (4)
  1. [Throughout] There are numerous typographical errors that should be cleaned up in a revision, including 'sttates' after Eq. (36), 'anther' in Section III, 'an more' in Section IV, 'Wiensner' in Section V.H, and a stray '9' in Eq. (7).
  2. [Tables III and VI] The recovery operations in the original Table III and the erratum Table VI are listed in different orders (e.g., (0,1,1) is σzσx in one and σxσz in the other). Since σx and σz anticommute, the sign convention matters; the authors should specify the ordering convention and verify that each tabulated operation actually returns the desired state.
  3. [Section XI] The conclusions contain an unfinished sentence: 'we also make some aspects of tripartite entanglement dealing with tripartite entanglement.' This should be rewritten to state what the section actually covers.
  4. [Section V.A opening note] Placing the sentence 'This section contains a mistake' at the start of the main text is an unusual way to handle an erratum; the corrected derivation should simply appear in the section, or the paper should refer to a properly formatted erratum.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the review's claims rest on standard external results and self-contained worked calculations; self-citations are ancillary.

full rationale

The paper is a review/tutorial rather than a prediction paper, so the main circularity failure modes (fitted parameters renamed as predictions, quantities defined in terms of the claimed output) do not apply. Its central claims about GHZ and W classes, nonlocality, and applications are supported by a large independent literature (e.g., Dür–Vidal–Cirac for SLOCC classes, Mermin and Svetlichny for nonlocality, Karlsson–Bourennane for GHZ teleportation, and many experimental references). The two author-overlapping citations, Refs. [66] and [221], are used as literature pointers: Ref. [66] is described as earlier work on GHZ-based error detection, and Ref. [221] is listed in the noisy-environment survey. The GHZ teleportation calculation in Section V.B is carried out directly in the text from the stated channel and measurement basis, Eqs. (51)–(75), without importing its final fidelity as an input; even if the algebra has issues, those are correctness defects rather than circular ones. The appended erratum explicitly flags Eq. (41) and Tables I–III of Section V.A as mistaken, which is an honest limitation statement and again not a circularity. No load-bearing step reduces by definition to its own input, and no fitted parameter is renamed as a prediction.

Assumptions & free parameters 0 free parameters · 3 assumptions · 0 invented entities

The paper introduces no free parameters fitted to data and no new physical entities. It relies on standard quantum mechanics and on the correctness of the literature it summarizes. The latter assumption is partially violated by the paper's own acknowledged teleportation mistake.

assumptions (3)
  • standard math The standard postulates of quantum mechanics, including the Hilbert space description of composite systems and projective measurements.
    Every section of the review assumes the conventional quantum formalism without questioning it, e.g., Section II uses Schmidt decomposition and Bell bases.
  • domain assumption The SLOCC classification of pure three-qubit states into two inequivalent classes, GHZ and W, is correct.
    Section III.A adopts the Dür-Vidal-Cirac classification as the organizing principle for the review.
  • domain assumption The summarized experimental and theoretical results from the cited literature are accurately represented.
    As a review, the paper depends on faithful reporting of prior work; the acknowledged error in Section V.A shows this assumption is not fully satisfied.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Tripartite entanglement: Foundations and applications." pith.science (2026). https://pith.science/paper/GLW5M4CI

@misc{pith2026190900862,
  author       = {Pith},
  title        = {Pith review of: Tripartite entanglement: Foundations and applications},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/GLW5M4CI}},
  note         = {Machine review of arXiv:1909.00862}
}
read the original abstract

We review some current ideas about tripartite entanglement, the case representing the next level of complexity beyond the simplest one (though far from trivial), namely the bipartite. This kind of entanglement has an essential role in the understanding of foundations of quantum mechanics. Also, it allows several applications in the fields of quantum information processing and quantum computing. In this paper, we make a revision about the main foundational aspects of tripartite entanglement and we discuss the possibility of using it as a resource to execute quantum protocols. We present some examples of quantum protocols in detail.

Figures

Figures reproduced from arXiv: 1909.00862 by the authors.

Figure 1
Figure 1. FIG. 1: All the possibilities of how entangle three qubits. From the top to the bellow: First, Genuine tripartite [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2: Bell nonlocality in a tripartite scenario. A source S emits three spin 1 [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3: A possible scheme to make a teleport of a qubit state by using a three-particle entangled state as the [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figures from the paper (5 more)
Figure 4
Figure 4. Figure 4: FIG. 4: Scheme to teleport a single qubit state by using a GHZ state as the quantum channel. A GHZ measurement [PITH_FULL_IMAGE:figures/full_fig_p011_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5: Graph of the quantum fidelity corresponding to the case of a single-qubit state teleport by using a GHZ [PITH_FULL_IMAGE:figures/full_fig_p013_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6: An EPR state can be teleported by using a GHZ state as the quantum channel. A measurement on GHZ [PITH_FULL_IMAGE:figures/full_fig_p014_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7: A possible scheme to teleport a GHZ state. Three EPR states are used as the quantum channel, and EPR [PITH_FULL_IMAGE:figures/full_fig_p014_7.png]
Figure 8
Figure 8. Figure 8: FIG. 8: A possible way to teleport a W state it is illustrated. A GHZ state and an EPR channel are used as the [PITH_FULL_IMAGE:figures/full_fig_p016_8.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

228 extracted references · 68 canonical work pages

  1. [1]

    M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information , 10th Anniversary edition published 2010, Vol. 1 (Cambridge university press, 2000)

    2010

  2. [2]

    Note though that entanglement is not the only non-classical resource useful for computation

  3. [3]

    Barnett, Quantum information, Vol

    S. Barnett, Quantum information, Vol. 16 (Oxford University Press, 2009)

    2009

  4. [4]

    Luo, H.-S

    Y.-H. Luo, H.-S. Zhong, M. Erhard, X.-L. Wang, L.-C. Peng, M. Krenn, X. Jiang, L. Li, N.-L. Liu, C.-Y. Lu, A. Zeilinger, and J.-W. Pan, Quantum teleportation in high dimensions, Phys. Rev. Lett. 123, 070505 (2019)

    2019

  5. [5]

    Chen, S.-Y

    P.-X. Chen, S.-Y. Zhu, and G.-C. Guo, General form of genuine multipartite entanglement quantum channels for telepor- tation, Phys. Rev. A 74, 032324 (2006)

    2006

  6. [6]

    A. S. De and U. Sen, Quantum advantage in communication networks, arXiv preprint arXiv:1105.2412 (2011)

    arXiv 2011

  7. [7]

    Raussendorf and H

    R. Raussendorf and H. J. Briegel, A one-way quantum computer, Phys. Rev. Lett. 86, 5188 (2001)

    2001

  8. [8]

    M. Li, L. Jia, J. Wang, S. Shen, and S.-M. Fei, Measure and detection of genuine multipartite entanglement for tripartite systems, Phys. Rev. A 96, 052314 (2017)

    2017

Show all 228 references
  1. [9]

    H. J. Briegel, D. E. Browne, W. D¨ ur, R. Raussendorf, and M. Van den Nest, Measurement-based quantum computation, Nature Physics 5, 19 (2009)

    2009

  2. [10]

    It is important to keep in mind that bipartite entanglement does not necessarily imply two spatially separated particles, instead it can be generated between different degrees of freedom in a single part [223]

  3. [11]

    Fortes and G

    R. Fortes and G. Rigolin, Fighting noise with noise in realistic quantum teleportation, Phys. Rev. A 92, 012338 (2015)

    2015

  4. [12]

    EPR, after Einstein, Podolski and Rosen’s seminal paper [224])

  5. [13]

    The symbol “∗”indicates complex conjugation of the associated matrix elements

  6. [14]

    R. F. Werner, Quantum states with einstein-podolsky-rosen correlations admitting a hidden-variable model, Phys. Rev. A 40, 4277 (1989)

    1989

  7. [15]

    p = tr (⏐⏐φ2 11 ⟩ ⟨ φ2 11 ⏐⏐ ˆρ ) = tr (⏐⏐φ2 11 ⟩ ⟨ φ2 11 ⏐⏐ ˆWp )

    Particularly in the case d = 2, p denotes the singlet fraction or in other words the degree of similarity of the state before (ˆρ) and after ( ˆWp) twirling operations, to the singlet state ⏐⏐φ2 11 ⟩ , i.e. p = tr (⏐⏐φ2 11 ⟩ ⟨ φ2 11 ⏐⏐ ˆρ ) = tr (⏐⏐φ2 11 ⟩ ⟨ φ2 11 ⏐⏐ ˆWp )

  8. [16]

    Horodecki and P

    M. Horodecki and P. Horodecki, Reduction criterion of separability and limits for a class of distillation protocols, Phys. Rev. A 59, 4206 (1999)

    1999

  9. [17]

    Brunner, D

    N. Brunner, D. Cavalcanti, S. Pironio, V. Scarani, and S. Wehner, Bell nonlocality, Reviews of Modern Physics 86, 419 (2014), arXiv:1303.2849

    2014 arXiv

  10. [18]

    Hirsch, M

    F. Hirsch, M. T. Quintino, T. V´ ertesi, M. Navascu´ es, and N. Brunner, Better local hidden variable models for two-qubit Werner states and an upper bound on the Grothendieck constant $K G(3)$, Quantum 1, 3 (2016), arXiv:1609.06114. 21

    2016 arXiv

  11. [19]

    M. J. Zhao, T. G. Zhang, X. Li-Jost, and S. M. Fei, Identification of three-qubit entanglement, Physical Review A - Atomic, Molecular, and Optical Physics 87, 012316 (2013)

    2013

  12. [20]

    S. Bose, V. Vedral, and P. L. Knight, Purification via entanglement swapping and conserved entanglement, Phys. Rev. A 60, 194 (1999)

    1999

  13. [21]

    Vidal, Entanglement of pure states for a single copy, Phys

    G. Vidal, Entanglement of pure states for a single copy, Phys. Rev. Lett. 83, 1046 (1999)

    1999

  14. [22]

    D¨ ur, G

    W. D¨ ur, G. Vidal, and J. I. Cirac, Three qubits can be entangled in two inequivalent ways, Phys. Rev. A 62, 062314 (2000)

    2000

  15. [23]

    D. M. Greenberger, M. A. Horne, A. Shimony, and A. Zeilinger, Bell’s theorem without inequalities, American Journal of Physics 58, 1131 (1990)

    1990

  16. [24]

    D. M. Greenberger, M. A. Horne, and A. Zeilinger, Going beyond bell’s theorem, in Bell’s theorem, quantum theory and conceptions of the universe (Springer, 1989) pp. 69–72

    1989

  17. [25]

    Zeilinger, M

    A. Zeilinger, M. A. Horne, and D. M. Greenberger, NASA Conf. Publ. No. 3135 (National Aeronautics and Space Administration, Code NTT, Washington, DC (1997)

    1997

  18. [26]

    ˙Zukowski, A

    M. ˙Zukowski, A. Zeilinger, M. Horne, and H. Weinfurter, Quest for ghz states, Acta Phys. Pol. A 93, 187 (1998)

    1998

  19. [27]

    Schwemmer, L

    C. Schwemmer, L. Knips, M. C. Tran, A. De Rosier, W. Laskowski, T. Paterek, and H. Weinfurter, Genuine multipartite entanglement without multipartite correlations, Physical review letters 114, 180501 (2015)

    2015

  20. [28]

    Ac´ ın, A

    A. Ac´ ın, A. Andrianov, L. Costa, E. Jan´ e, J. I. Latorre, and R. Tarrach, Generalized schmidt decomposition and classi- fication of three-quantum-bit states, Phys. Rev. Lett. 85, 1560 (2000)

    2000

  21. [29]

    Ac´ ın, A

    A. Ac´ ın, A. Andrianov, E. Jan´ e, and R. Tarrach, Three-qubit pure-state canonical forms, Journal of Physics A: Mathe- matical and General 34, 6725 (2001)

    2001

  22. [30]

    A. Acin, D. Bruß, M. Lewenstein, and A. Sanpera, Classification of mixed three-qubit states, Physical Review Letters 87, 040401 (2001)

    2001

  23. [31]

    Erhard, M

    M. Erhard, M. Malik, M. Krenn, and A. Zeilinger, Experimental greenberger–horne–zeilinger entanglement beyond qubits, Nature Photonics 12, 759 (2018)

    2018

  24. [32]

    Siewert and C

    J. Siewert and C. Eltschka, Quantifying tripartite entanglement of three-Qubit generalized Werner States, Physical Review Letters 108, 230502 (2012)

    2012

  25. [33]

    Aravind, Borromean entanglement of the ghz state, in Potentiality, entanglement and passion-at-a-distance (Springer,

    P. Aravind, Borromean entanglement of the ghz state, in Potentiality, entanglement and passion-at-a-distance (Springer,

  26. [34]

    Bengtsson and K

    I. Bengtsson and K. Zyczkowski, A brief introduction to multipartite entanglement, arXiv preprint arXiv:1612.07747 (2016)

    2016 arXiv

  27. [35]

    L. H. Kauffman and S. J. Lomonaco Jr, Quantum entanglement and topological entanglement, New Journal of Physics 4, 73 (2002)

    2002

  28. [36]

    Asoudeh, V

    M. Asoudeh, V. Karimipour, L. Memarzadeh, and A. Rezakhani, On a suggestion relating topological and quantum mechanical entanglements, Physics Letters A 327, 380 (2004)

    2004

  29. [37]

    Mironov, Topological entanglement and knots, Universe 5, 60 (2019)

    S. Mironov, Topological entanglement and knots, Universe 5, 60 (2019)

    2019

  30. [38]

    Perseguers, D

    S. Perseguers, D. Cavalcanti, G. Lapeyre Jr, M. Lewenstein, and A. Ac´ ın, Multipartite entanglement percolation, Physical Review A 81, 032327 (2010)

    2010

  31. [39]

    McCutcheon, A

    W. McCutcheon, A. Pappa, B. Bell, A. McMillan, A. Chailloux, T. Lawson, M. Mafu, D. Markham, E. Diamanti, I. Kerenidis, et al., Experimental verification of multipartite entanglement in quantum networks, Nature communications 7, 13251 (2016)

    2016

  32. [40]

    Duff, The black hole/qubit correspondence, in Journal of Physics: Conference Series , Vol

    M. Duff, The black hole/qubit correspondence, in Journal of Physics: Conference Series , Vol. 462 (IOP Publishing, 2013) p. 012012

    2013

  33. [41]

    Borsten, M

    L. Borsten, M. J. Duff, and P. L´ evay, The black-hole/qubit correspondence: an up-to-date review, Classical and Quantum Gravity 29, 224008 (2012)

    2012

  34. [42]

    The junction of both premises is known as local realism assumption

  35. [43]

    J. S. Bell, On the Einstein Podolsky Rosen paradox, Physics 1, 195 (1964)

    1964

  36. [44]

    N. D. Mermin, Quantum mysteries revisited, American Journal of Physics 58, 731 (1990)

    1990

  37. [45]

    H.-K. Lo, T. Spiller, and S. Popescu, Introduction to quantum computation and information (World Scientific, 1998)

    1998

  38. [46]

    Cabello, Bell’s theorem with and without inequalities for the three-qubit greenberger-horne-zeilinger and w states, Phys

    A. Cabello, Bell’s theorem with and without inequalities for the three-qubit greenberger-horne-zeilinger and w states, Phys. Rev. A 65, 032108 (2002)

    2002

  39. [47]

    Another interesting proof of the violation local realism without using Bell inequalities is given by the Hardy paradox [225]

  40. [48]

    N. D. Mermin, Extreme quantum entanglement in a superposition of macroscopically distinct states, Phys. Rev. Lett. 65, 1838 (1990)

    1990

  41. [49]

    Ardehali, Bell inequalities with a magnitude of violation that grows exponentially with the number of particles, Phys

    M. Ardehali, Bell inequalities with a magnitude of violation that grows exponentially with the number of particles, Phys. Rev. A 46, 5375 (1992)

    1992

  42. [50]

    A. V. Belinski˘ ı and D. N. Klyshko, Interference of light and bell’s theorem, Physics-Uspekhi 36, 653 (1993)

    1993

  43. [51]

    Svetlichny, Distinguishing three-body from two-body nonseparability by a bell-type inequality, Phys

    G. Svetlichny, Distinguishing three-body from two-body nonseparability by a bell-type inequality, Phys. Rev. D 35, 3066 (1987)

    1987

  44. [52]

    J. L. Cereceda, Three-particle entanglement versus three-particle nonlocality, Phys. Rev. A 66, 024102 (2002)

    2002

  45. [53]

    Bancal, J

    J.-D. Bancal, J. Barrett, N. Gisin, and S. Pironio, Definitions of multipartite nonlocality, Phys. Rev. A 88, 014102 (2013)

    2013

  46. [54]

    B. Paul, K. Mukherjee, and D. Sarkar, Revealing hidden genuine tripartite nonlocality, Physical Review A 94, 052101 (2016). 22

    2016

  47. [55]

    J.-W. Pan, D. Bouwmeester, M. Daniell, H. Weinfurter, and A. Zeilinger, Experimental test of quantum nonlocality in three-photon greenberger–horne–zeilinger entanglement, Nature 403, 515 (2000)

    2000

  48. [56]

    Lavoie, R

    J. Lavoie, R. Kaltenbaek, and K. J. Resch, Experimental violation of svetlichny’s inequality, New Journal of Physics 11, 073051 (2009)

    2009

  49. [57]

    Erven, E

    C. Erven, E. Meyer-Scott, K. Fisher, J. Lavoie, B. Higgins, Z. Yan, C. Pugh, J.-P. Bourgoin, R. Prevedel, L. Shalm, et al., Experimental three-photon quantum nonlocality under strict locality conditions, Nature photonics 8, 292 (2014)

    2014

  50. [58]

    Zhang, C.-J

    C. Zhang, C.-J. Zhang, Y.-F. Huang, Z.-B. Hou, B.-H. Liu, C.-F. Li, and G.-C. Guo, Experimental test of genuine multipartite nonlocality under the no-signalling principle, Scientific reports 6, 39327 (2016)

    2016

  51. [59]

    Singh and A

    P. Singh and A. Kumar, Analysing nonlocality robustness in multiqubit systems under noisy conditions and weak mea- surements, Quantum Information Processing 17, 249 (2018)

    2018

  52. [60]

    Swain, A

    M. Swain, A. Rai, B. K. Behera, and P. K. Panigrahi, Experimental demonstration of the violations of mermin’s and svetlichny’s inequalities for w and ghz states, Quantum Information Processing 18, 218 (2019)

    2019

  53. [61]

    Caban and K

    P. Caban and K. Trzci´ nska, Noise resistance of activation of the violation of the svetlichny inequality, Quantum Information Processing 18, 139 (2019)

    2019

  54. [62]

    Chaves, D

    R. Chaves, D. Cavalcanti, and L. Aolita, Causal hierarchy of multipartite Bell nonlocality, Quantum 1, 23 (2017)

    2017

  55. [63]

    Karlsson and M

    A. Karlsson and M. Bourennane, Quantum teleportation using three-particle entanglement, Physical Review A 58, 4394 (1998)

    1998

  56. [64]

    Almeida, L

    N. Almeida, L. Maia, C. Villas-Bˆ oas, and M. Moussa, One-cavity scheme for atomic-state teleportation through ghz states, Physics Letters A 241, 213 (1998)

    1998

  57. [65]

    B. S. Choudhury and S. Samanta, Simultaneous perfect teleportation of three 2-qubit states, Quantum Information Processing 16, 230 (2017)

    2017

  58. [66]

    Moreno, A

    M. Moreno, A. Fonseca, and M. M. Cunha, Using three-partite ghz states for partial quantum error detection in entanglement-based protocols, Quantum Information Processing 17, 191 (2018)

    2018

  59. [67]

    Man, Y.-J

    Z.-X. Man, Y.-J. Xia, and N. B. An, Quantum state sharing of an arbitrary multiqubit state using nonmaximally entangled ghz states, The European Physical Journal D 42, 333 (2007)

    2007

  60. [68]

    Wang, Y.-T

    Z.-Y. Wang, Y.-T. Gou, J.-X. Hou, L.-K. Cao, and X.-H. Wang, Probabilistic resumable quantum teleportation of a two-qubit entangled state, Entropy 21, 352 (2019)

    2019

  61. [69]

    Gorbachev and A

    V. Gorbachev and A. Trubilko, Quantum teleportation of an einstein-podolsy-rosen pair using an entangled three-particle state, Journal of Experimental and Theoretical Physics 91, 894 (2000)

    2000

  62. [70]

    Shi, Y.-K

    B.-S. Shi, Y.-K. Jiang, and G.-C. Guo, Probabilistic teleportation of two-particle entangled state, Physics Letters A 268, 161 (2000)

    2000

  63. [71]

    Tsai and T

    C.-W. Tsai and T. Hwang, Teleportation of a pure epr state via ghz-like state, International Journal of Theoretical Physics 49, 1969 (2010)

    2010

  64. [72]

    Li, R.-j

    D.-f. Li, R.-j. Wang, and E. Baagyere, Quantum teleportation of an arbitrary two-qubit state by using two three-qubit ghz states and the six-qubit entangled state, Quantum Information Processing 18, 147 (2019)

    2019

  65. [73]

    Dai, P.-X

    H.-Y. Dai, P.-X. Chen, and C.-Z. Li, Probabilistic teleportation of an arbitrary two-particle state by a partially entangled three-particle ghz state and w state, Optics communications 231, 281 (2004)

    2004

  66. [74]

    Wang, X.-T

    K. Wang, X.-T. Yu, and Z.-C. Zhang, Teleportation of two-qubit entangled state via non-maximally entangled ghz state, Procedia computer science 131, 1202 (2018)

    2018

  67. [75]

    Hassanpour and M

    S. Hassanpour and M. Houshmand, Bidirectional teleportation of a pure epr state by using ghz states, Quantum Infor- mation Processing 15, 905 (2016)

    2016

  68. [76]

    Zou, X.-T

    Z.-Z. Zou, X.-T. Yu, Y.-X. Gong, and Z.-C. Zhang, Multihop teleportation of two-qubit state via the composite ghz–bell channel, Physics Letters A 381, 76 (2017)

    2017

  69. [77]

    Wang, X.-T

    K. Wang, X.-T. Yu, X.-F. Cai, and Z.-C. Zhang, Probabilistic teleportation of arbitrary two-qubit quantum state via non-symmetric quantum channel, Entropy 20, 238 (2018)

    2018

  70. [78]

    Y. Xia, J. Song, P.-M. Lu, and H.-S. Song, Teleportation of an n-photon greenberger-horne-zeilinger (ghz) polarization- entangled state using linear optical elements, JOSA B 27, A1 (2010)

    2010

  71. [79]

    Hong, Probabilistic teleportation of the three-particle entangled state via entanglement swapping, Chinese Physics Letters 18, 1004 (2001)

    L. Hong, Probabilistic teleportation of the three-particle entangled state via entanglement swapping, Chinese Physics Letters 18, 1004 (2001)

    2001

  72. [80]

    Xiu and L

    L. Xiu and L. Hong-Cai, Probabilistic teleportation of a three-particle ghz state via two three-particle entangled w states, Communications in Theoretical Physics 45, 1018 (2006)

    2006

  73. [81]

    B. S. Choudhury and S. Samanta, A teleportation protocol for transfer of arbitrary ghz-states using intermediate nodes, International Journal of Theoretical Physics 57, 2665 (2018)

    2018

  74. [82]

    Jin-Ming and G

    L. Jin-Ming and G. Guang-Can, Quantum teleportation of a three-particle entangled state, Chinese Physics Letters 19, 456 (2002)

    2002

  75. [83]

    J. Fang, Y. Lin, S. Zhu, and X. Chen, Probabilistic teleportation of a three-particle state via three pairs of entangled particles, Physical Review A 67, 014305 (2003)

    2003

  76. [84]

    Shi and A

    B.-S. Shi and A. Tomita, Teleportation of an unknown state by w state, Physics Letters A 296, 161 (2002)

    2002

  77. [85]

    teleportation of an unknown state by w states

    J. Joo and Y.-J. Park, Comment on “teleportation of an unknown state by w states”:[phys. lett. a 296 (2002) 161], Physics Letters A 300, 324 (2002)

    2002

  78. [86]

    comment on: Teleportation of an unknown state by w state

    B.-S. Shi and A. Tomita, Reply to“comment on: Teleportation of an unknown state by w state”.[phys. lett. a 300 (2002) 324], Physics Letters A 300, 538 (2002)

    2002

  79. [87]

    Gorbachev, A

    V. Gorbachev, A. Trubilko, A. Rodichkina, and A. Zhiliba, Can the states of the w-class be suitable for teleportation?, Physics Letters A 314, 267 (2003). 23

    2003

  80. [88]

    Joo, Y.-J

    J. Joo, Y.-J. Park, S. Oh, and J. Kim, Quantum teleportation via a w state, New Journal of Physics 5, 136 (2003)

    2003

  81. [89]

    Agrawal and A

    P. Agrawal and A. Pati, Perfect teleportation and superdense coding with w states, Phys. Rev. A 74, 062320 (2006)

    2006

  82. [90]

    Li and D

    L. Li and D. Qiu, The states of w-class as shared resources for perfect teleportation and superdense coding, Journal of Physics A: Mathematical and Theoretical 40, 10871 (2007)

    2007

  83. [91]

    Zhang, L

    Z.-h. Zhang, L. Shu, and Z.-w. Mo, Quantum teleportation and superdense coding through the composite w-bell channel, Quantum information processing 12, 1957 (2013)

    2013

  84. [92]

    Yi-Zhuang, G

    Z. Yi-Zhuang, G. Yong-Jian, and G. Guang-Can, Teleportation of a three-particle entangled w state, Chinese Physics 11, 537 (2002)

    2002

  85. [93]

    X. Gao, Z. Zhang, Y. Gong, B. Sheng, and X. Yu, Teleportation of entanglement using a three-particle entangled w state, JOSA B 34, 142 (2017)

    2017

  86. [94]

    Guo, B.-H

    Y. Guo, B.-H. Liu, C.-F. Li, and G.-C. Guo, Advances in quantum dense coding, Advanced Quantum Technologies 2, 1900011 (2019), https://onlinelibrary.wiley.com/doi/pdf/10.1002/qute.201900011

    2019 doi

  87. [95]

    Hao, C.-F

    J.-C. Hao, C.-F. Li, and G.-C. Guo, Controlled dense coding using the greenberger-horne-zeilinger state, Physical Review A 63, 054301 (2001)

    2001

  88. [96]

    Huang, S.-S

    Y.-B. Huang, S.-S. Li, and Y.-Y. Nie, Controlled dense coding via ghz-class state, International Journal of Modern Physics C 19, 1509 (2008)

    2008

  89. [97]

    Yang, M.-q

    X. Yang, M.-q. Bai, and Z.-w. Mo, Controlled dense coding with the w state, International Journal of Theoretical Physics 56, 3525 (2017)

    2017

  90. [98]

    Y.-S. Zhou, F. Wang, and M.-X. Luo, Efficient superdense coding with w states, International Journal of Theoretical Physics 57, 1935 (2018)

    2018

  91. [99]

    Ye and L.-B

    L. Ye and L.-B. Yu, Scheme for implementing quantum dense coding using tripartite entanglement in cavity qed, Physics Letters A 346, 330 (2005)

    2005

  92. [100]

    S. Roy, T. Chanda, T. Das, A. S. De, and U. Sen, Deterministic quantum dense coding networks, Physics Letters A 382, 1709 (2018)

    2018

  93. [101]

    Wiesner, Conjugate coding, ACM Sigact News 15, 78 (1983)

    S. Wiesner, Conjugate coding, ACM Sigact News 15, 78 (1983)

    1983

  94. [102]

    C. H. Bennett and G. Brassard, Quantum cryptography: public key distribution and coin tossing., Theor. Comput. Sci. 560, 7 (2014)

    2014

  95. [103]

    A. K. Ekert, Quantum cryptography based on bell’s theorem, Physical review letters 67, 661 (1991)

    1991

  96. [104]

    Hillery, V

    M. Hillery, V. Buˇ zek, and A. Berthiaume, Quantum secret sharing, Physical Review A 59, 1829 (1999)

    1999

  97. [105]

    J. Joo, J. Lee, J. Jang, and Y.-J. Park, Quantum secure communication with w states, arXiv preprint quant-ph/0204003 (2002)

    2002 arXiv

  98. [106]

    X.-R. Jin, X. Ji, Y.-Q. Zhang, S. Zhang, S.-K. Hong, K.-H. Yeon, and C.-I. Um, Three-party quantum secure direct communication based on ghz states, Physics Letters A 354, 67 (2006)

    2006

  99. [107]

    Man, Y.-J

    Z.-X. Man, Y.-J. Xia, and N. B. An, Quantum secure direct communication by using ghz states and entanglement swapping, Journal of Physics B: Atomic, Molecular and Optical Physics 39, 3855 (2006)

    2006

  100. [108]

    Chen, Q.-Y

    X.-B. Chen, Q.-Y. Wen, F.-Z. Guo, Y. Sun, G. Xu, and F.-C. Zhu, Controlled quantum secure direct communication with w state, International Journal of Quantum Information 6, 899 (2008)

    2008

  101. [109]

    Christandl and S

    M. Christandl and S. Wehner, Quantum anonymous transmissions, in International Conference on the Theory and Ap- plication of Cryptology and Information Security (Springer, 2005) pp. 217–235

    2005

  102. [110]

    Lipinska, G

    V. Lipinska, G. Murta, and S. Wehner, Anonymous transmission in a noisy quantum network using the w state, Physical Review A 98, 052320 (2018)

    2018

  103. [111]

    D. Cruz, R. Fournier, F. Gremion, A. Jeannerot, K. Komagata, T. Tosic, J. Thiesbrummel, C. L. Chan, N. Macris, M.-A. Dupertuis, et al., Efficient quantum algorithms for ghz and w states, and implementation on the ibm quantum computer, Advanced Quantum Technologies 2, 1900015 (2019)

    2019

  104. [112]

    Hwang, D

    M.-R. Hwang, D. Park, and E. Jung, Tripartite entanglement in a noninertial frame, Phys. Rev. A 83, 012111 (2011)

    2011

  105. [113]

    A. Acin, E. Jane, W. D¨ ur, and G. Vidal, Optimal distillation of a greenberger-horne-zeilinger state, Physical review letters 85, 4811 (2000)

    2000

  106. [114]

    Mo, C.-F

    Y.-N. Mo, C.-F. Li, and G.-C. Guo, Distillation of the greenberger-horne-zeilinger state from arbitrary tripartite states, Phys. Rev. A 65, 024301 (2002)

    2002

  107. [115]

    Yildiz, Optimal distillation of three-qubit w states, Physical Review A 82, 012317 (2010)

    A. Yildiz, Optimal distillation of three-qubit w states, Physical Review A 82, 012317 (2010)

    2010

  108. [116]

    Liao, M.-F

    X.-P. Liao, M.-F. Fang, and J.-S. Fang, Entanglement purification and amplification of three-qubit states using two- outcome weak measurements, Journal of Modern Optics 61, 1018 (2014)

    2014

  109. [117]

    J. Yuan, S. Tang, X. Wang, and D. Zhang, One-step distillation of local-unitary-equivalent ghz-type states, Quantum Information Processing 17, 259 (2018)

    2018

  110. [118]

    Gottesman and I

    D. Gottesman and I. L. Chuang, Demonstrating the viability of universal quantum computation using teleportation and single-qubit operations, Nature 402, 390 (1999)

    1999

  111. [119]

    Y. Cai, H. N. Le, and V. Scarani, State complexity and quantum computation, Annalen der Physik 527, 684 (2015), https://onlinelibrary.wiley.com/doi/pdf/10.1002/andp.201400199

    2015 doi

  112. [120]

    D’Hondt and P

    E. D’Hondt and P. Panangaden, The computational power of the w and ghz states, Quantum Info. Comput.6, 173 (2006)

    2006

  113. [121]

    Rajan and M

    D. Rajan and M. Visser, Quantum blockchain using entanglement in time, Quantum Reports 1, 3 (2019)

    2019

  114. [122]

    Zhao, Y.-A

    Z. Zhao, Y.-A. Chen, A.-N. Zhang, T. Yang, H. J. Briegel, and J.-W. Pan, Experimental demonstration of five-photon entanglement and open-destination teleportation, Nature 430, 54 (2004)

    2004

  115. [123]

    T. Monz, P. Schindler, J. T. Barreiro, M. Chwalla, D. Nigg, W. A. Coish, M. Harlander, W. H¨ ansel, M. Hennrich, and R. Blatt, 14-qubit entanglement: Creation and coherence, Physical Review Letters 106, 130506 (2011). 24

    2011

  116. [124]

    Bouwmeester, J.-W

    D. Bouwmeester, J.-W. Pan, M. Daniell, H. Weinfurter, and A. Zeilinger, Observation of three-photon greenberger-horne- zeilinger entanglement, Physical Review Letters 82, 1345 (1999)

    1999

  117. [125]

    M. Eibl, N. Kiesel, M. Bourennane, C. Kurtsiefer, and H. Weinfurter, Experimental realization of a three-qubit entangled w state, Phys. Rev. Lett. 92, 077901 (2004)

    2004

  118. [126]

    Zeilinger, M

    A. Zeilinger, M. A. Horne, H. Weinfurter, and M. ˙Zukowski, Three-particle entanglements from two entangled pairs, Physical review letters 78, 3031 (1997)

    1997

  119. [127]

    Laflamme, E

    R. Laflamme, E. Knill, W. Zurek, P. Catasti, and S. Mariappan, Nmr greenberger–horne–zeilinger states, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences356, 1941 (1998)

    1998

  120. [128]

    L. Ju, M. Yang, N. Paunkovi´ c, W.-J. Chu, and Z.-L. Cao, Creating photonic ghz and w states via quantum walk, Quantum Information Processing 18, 176 (2019)

    2019

  121. [129]

    Erd¨ osi, M

    D. Erd¨ osi, M. Huber, B. C. Hiesmayr, and Y. Hasegawa, Proving the generation of genuine multipartite entanglement in a single-neutron interferometer experiment, New Journal of Physics 15, 023033 (2013)

    2013

  122. [130]

    Yamamoto, K

    T. Yamamoto, K. Tamaki, M. Koashi, and N. Imoto, Polarization-entangled w state using parametric down-conversion, Physical Review A 66, 064301 (2002)

    2002

  123. [131]

    C.-s. Yu, X. X. Yi, H.-s. Song, and D. Mei, Robust preparation of greenberger-horne-zeilinger andw states of three distant atoms, Phys. Rev. A 75, 044301 (2007)

    2007

  124. [132]

    Z. J. Deng, M. Feng, and K. L. Gao, Simple scheme for generating an n-qubit w state in cavity qed, Phys. Rev. A 73, 014302 (2006)

    2006

  125. [133]

    Gorbachev, A

    V. Gorbachev, A. Rodichkina, A. Trubilko, and A. Zhiliba, On preparation of the entangled w-states from atomic ensem- bles, Physics Letters A 310, 339 (2003)

    2003

  126. [134]

    C. F. Roos, M. Riebe, H. H¨ affner, W. H¨ ansel, J. Benhelm, G. P. Lancaster, C. Becher, F. Schmidt-Kaler, and R. Blatt, Control and measurement of three-qubit entangled states, science 304, 1478 (2004)

    2004

  127. [135]

    Y.-H. Kang, Y. Xia, and P.-M. Lu, Effective scheme for preparation of a spin-qubit greenberger–horne–zeilinger state and w state in a quantum-dot-microcavity system, JOSA B 32, 1323 (2015)

    2015

  128. [136]

    Kang, Y.-H

    Y.-H. Kang, Y.-H. Chen, Q.-C. Wu, B.-H. Huang, J. Song, and Y. Xia, Fast generation of w states of superconducting qubits with multiple schr¨ odinger dynamics, Scientific reports6, 36737 (2016)

    2016

  129. [137]

    Chen and L.-T

    R.-X. Chen and L.-T. Shen, Tripartite entanglement of atoms trapped in coupled cavities via quantum zeno dynamics, Physics Letters A 375, 3840 (2011)

    2011

  130. [138]

    S. R. Miry, M. K. Tavassoly, and R. Roknizadeh, Generation of some entangled states of the cavity field, Quantum Information Processing 14, 593 (2015)

    2015

  131. [139]

    D. R. Hamel, L. K. Shalm, H. H¨ ubel, A. J. Miller, F. Marsili, V. B. Verma, R. P. Mirin, S. W. Nam, K. J. Resch, and T. Jennewein, Direct generation of three-photon polarization entanglement, Nature Photonics 8, 801 (2014)

    2014

  132. [140]

    B. d. L. Bernardo, M. Lenc´ ses, S. Brito, and A. Canabarro, Greenberger-horne-zeilinger state generation with linear optical elements, arXiv preprint arXiv:1811.10544 (2018)

    2018 arXiv

  133. [141]

    J. Heo, C. Hong, S.-G. Choi, and J.-P. Hong, Scheme for generation of three-photon entangled w state assisted by cross-kerr nonlinearity and quantum dot, Scientific reports 9, 10151 (2019)

    2019

  134. [142]

    Bellomo, R

    B. Bellomo, R. Lo Franco, and G. Compagno, n identical particles and one particle to entangle them all, Phys. Rev. A 96, 022319 (2017)

    2017

  135. [143]

    Yesilyurt, S

    C. Yesilyurt, S. Bugu, F. Ozaydin, A. A. Altintas, M. Tame, L. Yang, and S ¸ahin Kaya ¨Ozdemir, Deterministic local doubling of w states, J. Opt. Soc. Am. B 33, 2313 (2016)

    2016

  136. [144]

    Li, T.-Y

    D.-X. Li, T.-Y. Zheng, and X.-Q. Shao, Adiabatic preparation of multipartite ghz states via rydberg ground-state blockade, Optics Express 27, 20874 (2019)

    2019

  137. [145]

    Omran, H

    A. Omran, H. Levine, A. Keesling, G. Semeghini, T. T. Wang, S. Ebadi, H. Bernien, A. S. Zibrov, H. Pichler, S. Choi, et al., Generation and manipulation of schr\” odinger cat states in rydberg atom arrays, arXiv preprint arXiv:1905.05721 (2019)

    2019 arXiv

  138. [146]

    G¨ uhne and G

    O. G¨ uhne and G. T´ oth, Entanglement detection, Physics Reports474, 1 (2009)

    2009

  139. [147]

    D. Bruß, J. I. Cirac, P. Horodecki, F. Hulpke, B. Kraus, M. Lewenstein, and A. Sanpera, Reflections upon separability and distillability, Journal of Modern Optics 49, 1399 (2002)

    2002

  140. [148]

    Gerke, W

    S. Gerke, W. Vogel, and J. Sperling, Numerical construction of multipartite entanglement witnesses, Phys. Rev. X 8, 031047 (2018)

    2018

  141. [149]

    Pan and A

    J.-w. Pan and A. Zeilinger, Greenberger-horne-zeilinger-state analyzer, Physical Review A 57, 2208 (1998)

    1998

  142. [150]

    Qian, X.-L

    J. Qian, X.-L. Feng, and S.-Q. Gong, Universal greenberger-horne-zeilinger-state analyzer based on two-photon polariza- tion parity detection, Physical Review A 72, 052308 (2005)

    2005

  143. [151]

    Here, QND means a Quantum Non-demolition, related with the idea of a QND measurement [226]

  144. [152]

    Wang, D.-Y

    X.-W. Wang, D.-Y. Zhang, S.-Q. Tang, and L.-J. Xie, Nondestructive greenberger-horne-zeilinger-state analyzer, Quantum information processing 12, 1065 (2013)

    2013

  145. [153]

    More details can be accessed in [227, 228]

    Hyperentanglement it is a type of entanglement dealing with multiple different degrees of freedom of a system. More details can be accessed in [227, 228]

  146. [154]

    S. Song, Y. Cao, Y.-B. Sheng, and G.-L. Long, Complete greenberger–horne–zeilinger state analyzer using hyperentan- glement, Quantum information processing 12, 381 (2013)

    2013

  147. [155]

    Zheng, L.-X

    Y.-Y. Zheng, L.-X. Liang, and M. Zhang, Self-assisted complete analysis of three-photon hyperentangled greenberger– horne–zeilinger states with nitrogen-vacancy centers in microcavities, Quantum Information Processing 17, 172 (2018)

    2018

  148. [156]

    Habibian, J

    H. Habibian, J. W. Clark, N. Behbood, and K. Hingerl, Greenberger-horne-zeilinger and w entanglement witnesses for 25 the noninteracting fermi gas, Phys. Rev. A 81, 032302 (2010)

    2010

  149. [157]

    Chen, L.-z

    X.-y. Chen, L.-z. Jiang, P. Yu, and M. Tian, Necessary and sufficient fully separable criterion and entanglement of three-qubit greenberger–horne–zeilinger diagonal states, Quantum Information Processing 14, 2463 (2015)

    2015

  150. [158]

    M. Li, J. Wang, S. Shen, Z. Chen, and S.-M. Fei, Detection and measure of genuine tripartite entanglement with partial transposition and realignment of density matrices, Scientific reports 7, 17274 (2017)

    2017

  151. [159]

    Singh, H

    A. Singh, H. Singh, K. Dorai, et al., Experimental classification of entanglement in arbitrary three-qubit pure states on an nmr quantum information processor, Physical Review A 98, 032301 (2018)

    2018

  152. [160]

    Singh, K

    A. Singh, K. Dorai, et al., Experimentally identifying the entanglement class of pure tripartite states, Quantum Informa- tion Processing 17, 334 (2018)

    2018

  153. [161]

    Gross, Y.-K

    D. Gross, Y.-K. Liu, S. T. Flammia, S. Becker, and J. Eisert, Quantum state tomography via compressed sensing, Phys. Rev. Lett. 105, 150401 (2010)

    2010

  154. [162]

    K. J. Resch, P. Walther, and A. Zeilinger, Full characterization of a three-photon greenberger-horne-zeilinger state using quantum state tomography, Phys. Rev. Lett. 94, 070402 (2005)

    2005

  155. [163]

    Lu, J.-Q

    H.-X. Lu, J.-Q. Zhao, and X.-Q. Wang, Characterization of a high-intensity three-qubit ghz state using state tomography and gisin’s inequality, Physics Letters A 375, 1850 (2011)

    2011

  156. [164]

    Mikami, Y

    H. Mikami, Y. Li, K. Fukuoka, and T. Kobayashi, New high-efficiency source of a three-photon w state and its full characterization using quantum state tomography, Phys. Rev. Lett. 95, 150404 (2005)

    2005

  157. [165]

    Shi and Y.-B

    J. Shi and Y.-B. Zhan, Scheme for asymmetric and deterministic controlled bidirectional joint remote state preparation, Communications in Theoretical Physics 70, 515 (2018)

    2018

  158. [166]

    Sun, X.-B

    Y.-R. Sun, X.-B. Chen, G. Xu, K.-G. Yuan, and Y.-X. Yang, Asymmetric controlled bidirectional remote preparation of two-and three-qubit equatorial state, Scientific reports 9, 2081 (2019)

    2019

  159. [167]

    Kurpiers, P

    P. Kurpiers, P. Magnard, T. Walter, B. Royer, M. Pechal, J. Heinsoo, Y. Salath´ e, A. Akin, S. Storz, J.-C. Besse, et al., Deterministic quantum state transfer and remote entanglement using microwave photons, Nature 558, 264 (2018)

    2018

  160. [168]

    Dai, P.-X

    H.-Y. Dai, P.-X. Chen, L.-M. Liang, and C.-Z. Li, Classical communication cost and remote preparation of the four-particle ghz class state, Physics Letters A 355, 285 (2006)

    2006

  161. [169]

    Luo, X.-B

    M.-X. Luo, X.-B. Chen, S.-Y. Ma, X.-X. Niu, and Y.-X. Yang, Joint remote preparation of an arbitrary three-qubit state, Optics Communications 283, 4796 (2010)

    2010

  162. [170]

    Zhan and P

    Y.-B. Zhan and P. C. Ma, Deterministic joint remote preparation of arbitrary two-and three-qubit entangled states, Quantum information processing 12, 997 (2013)

    2013

  163. [171]

    A. H. Khosa, F. Saif, et al. , Remote preparation of atomic and field cluster states from a pair of tri-partite ghz states, Chinese Physics B 19, 040309 (2010)

    2010

  164. [172]

    N. B. An, Joint remote state preparation via w and w-type states, Optics Communications 283, 4113 (2010)

    2010

  165. [173]

    B. S. Choudhury and A. Dhara, Joint remote state preparation for two-qubit equatorial states, Quantum Information Processing 14, 373 (2015)

    2015

  166. [174]

    Wang, Classical communication cost and probabilistic remote two-qubit state preparation via povm and w-type states, Quantum Information Processing 11, 1585 (2012)

    Z.-y. Wang, Classical communication cost and probabilistic remote two-qubit state preparation via povm and w-type states, Quantum Information Processing 11, 1585 (2012)

    2012

  167. [175]

    D. Wang, R. Hoehn, L. Ye, and S. Kais, Generalized remote preparation of arbitrary m-qubit entangled states via genuine entanglements, Entropy 17, 1755 (2015)

    2015

  168. [176]

    Ra, H.-T

    Y.-S. Ra, H.-T. Lim, and Y.-H. Kim, Remote preparation of three-photon entangled states via single-photon measurement, Phys. Rev. A 94, 042329 (2016)

    2016

  169. [177]

    Lv, Z.-W

    S.-X. Lv, Z.-W. Zhao, and P. Zhou, Multiparty-controlled joint remote preparation of an arbitrary m-qudit state with d-dimensional greenberger-horne-zeilinger states, International Journal of Theoretical Physics 57, 148 (2018)

    2018

  170. [178]

    Xia, Q.-Q

    Y. Xia, Q.-Q. Chen, and N. B. An, Deterministic joint remote preparation of an arbitrary three-qubit state via einstein– podolsky–rosen pairs with a passive receiver, Journal of Physics A: Mathematical and Theoretical 45, 335306 (2012)

    2012

  171. [179]

    Luo, X.-B

    M.-X. Luo, X.-B. Chen, S.-Y. Ma, Y.-X. Yang, and Z.-M. Hu, Deterministic remote preparation of an arbitrary w-class state with multiparty, Journal of Physics B: Atomic, Molecular and Optical Physics 43, 065501 (2010)

    2010

  172. [180]

    Peng-Cheng and Z

    M. Peng-Cheng and Z. You-Bang, Scheme for probabilistic remotely preparing a multi-particle entangled ghz state, Chinese Physics B 17, 445 (2008)

    2008

  173. [181]

    Wang, Y.-D

    D. Wang, Y.-D. Hu, Z.-Q. Wang, and L. Ye, Efficient and faithful remote preparation of arbitrary three-and four-particle -class entangled states, Quantum Information Processing 14, 2135 (2015)

    2015

  174. [182]

    Wu and M

    N.-N. Wu and M. Jiang, A highly efficient scheme for joint remote preparation of multi-qubit w state with minimum quantum resource, Quantum Information Processing 17, 340 (2018)

    2018

  175. [183]

    Sang, Deterministic joint remote state preparation of an arbitrary equatorial three-qubit state, International Journal of Theoretical Physics 58, 1157 (2019)

    Z.-w. Sang, Deterministic joint remote state preparation of an arbitrary equatorial three-qubit state, International Journal of Theoretical Physics 58, 1157 (2019)

    2019

  176. [184]

    B. S. Choudhury and S. Samanta, Remote preparation of some three particle entangled states under divided information, International Journal of Theoretical Physics 58, 83 (2019)

    2019

  177. [185]

    Eisert and M

    J. Eisert and M. Plenio, Introduction to the basics of entanglement theory in continuous-variable systems, International Journal of Quantum Information 1, 479 (2003)

    2003

  178. [186]

    Adesso and F

    G. Adesso and F. Illuminati, Entanglement in continuous-variable systems: recent advances and current perspectives, Journal of Physics A: Mathematical and Theoretical 40, 7821 (2007)

    2007

  179. [187]

    S. L. Braunstein and H. J. Kimble, Teleportation of continuous quantum variables, Phys. Rev. Lett. 80, 869 (1998). 26

    1998

  180. [188]

    W. P. Bowen, N. Treps, B. C. Buchler, R. Schnabel, T. C. Ralph, H.-A. Bachor, T. Symul, and P. K. Lam, Experimental investigation of continuous-variable quantum teleportation, Phys. Rev. A 67, 032302 (2003)

    2003

  181. [189]

    R. E. S. Polkinghorne and T. C. Ralph, Continuous variable entanglement swapping, Phys. Rev. Lett. 83, 2095 (1999)

    1999

  182. [190]

    Takeda, M

    S. Takeda, M. Fuwa, P. van Loock, and A. Furusawa, Entanglement swapping between discrete and continuous variables, Phys. Rev. Lett. 114, 100501 (2015)

    2015

  183. [191]

    van Loock and A

    P. van Loock and A. Furusawa, Detecting genuine multipartite continuous-variable entanglement, Phys. Rev. A67, 052315 (2003)

    2003

  184. [192]

    Adesso, S

    G. Adesso, S. Ragy, and A. R. Lee, Continuous variable quantum information: Gaussian states and beyond, Open Systems & Information Dynamics 21, 1440001 (2014)

    2014

  185. [193]

    Adesso, A

    G. Adesso, A. Serafini, and F. Illuminati, Multipartite entanglement in three-mode gaussian states of continuous-variable systems: Quantification, sharing structure, and decoherence, Phys. Rev. A 73, 032345 (2006)

    2006

  186. [194]

    T. Aoki, N. Takei, H. Yonezawa, K. Wakui, T. Hiraoka, A. Furusawa, and P. van Loock, Experimental creation of a fully inseparable tripartite continuous-variable state, Physical review letters 91, 080404 (2003)

    2003

  187. [195]

    Coelho, F

    A. Coelho, F. Barbosa, K. Cassemiro, A. Villar, M. Martinelli, and P. Nussenzveig, Three-color entanglement, Science 326, 823 (2009)

    2009

  188. [196]

    L. K. Shalm, D. R. Hamel, Z. Yan, C. Simon, K. J. Resch, and T. Jennewein, Three-photon energy–time entanglement, Nature Physics 9, 19 (2013)

    2013

  189. [197]

    A. A. Valido, F. Levi, and F. Mintert, Hierarchies of multipartite entanglement for continuous-variable states, Phys. Rev. A 90, 052321 (2014)

    2014

  190. [198]

    Liang, J.-M

    H.-Q. Liang, J.-M. Liu, S.-S. Feng, and J.-G. Chen, Quantum teleportation with partially entangled states via noisy channels, Quantum information processing 12, 2671 (2013)

    2013

  191. [199]

    Fortes and G

    R. Fortes and G. Rigolin, Probabilistic quantum teleportation in the presence of noise, Phys. Rev. A 93, 062330 (2016)

    2016

  192. [200]

    Zhao, L.-Z

    J.-Q. Zhao, L.-Z. Cao, Y. Yang, Y.-D. Li, and H.-X. Lu, Tripartite entanglement and non-locality in three-qubit greenberger–horne–zeilinger states with bit-flip noise, Canadian Journal of Physics 97, 248 (2018)

    2018

  193. [201]

    Aolita, R

    L. Aolita, R. Chaves, D. Cavalcanti, A. Ac´ ın, and L. Davidovich, Scaling laws for the decay of multiqubit entanglement, Phys. Rev. Lett. 100, 080501 (2008)

    2008

  194. [202]

    L. T. Kenfack, M. Tchoffo, and L. C. Fai, Decoherence and protection of entanglement of a system of three qubits driven by a classical gaussian distributed fluctuating field, Physics Letters A 382, 2805 (2018)

    2018

  195. [203]

    Guo, J.-M

    H. Guo, J.-M. Liu, C.-J. Zhang, and C. Oh, Quantum discord of a three-qubit w-class state in noisy environments, Quantum Information and Computation 12, 677 (2012)

    2012

  196. [204]

    Mahdian, R

    M. Mahdian, R. Yousefjani, and S. Salimi, Quantum discord evolution of three-qubit states under noisy channels, The European Physical Journal D 66, 133 (2012)

    2012

  197. [205]

    Metwally and A

    N. Metwally and A. Almannaei, Dynamics of three-qubit systems in a noisy environment, Canadian Journal of Physics 94, 170 (2015)

    2015

  198. [206]

    T. K. Lionel, T. Martin, F. G. Collince, and L. C. Fai, Effects of static noise on the dynamics of quantum correlations for a system of three qubits, International Journal of Modern Physics B 31, 1750046 (2017)

    2017

  199. [207]

    Jung, M.-R

    E. Jung, M.-R. Hwang, Y. H. Ju, M.-S. Kim, S.-K. Yoo, H. Kim, D. Park, J.-W. Son, S. Tamaryan, and S.-K. Cha, Greenberger-horne-zeilinger versus w states: Quantum teleportation through noisy channels, Phys. Rev. A 78, 012312 (2008)

    2008

  200. [208]

    Hu, Robustness of greenberger–horne–zeilinger and w states for teleportation in external environments, Physics Letters A 375, 922 (2011)

    M.-L. Hu, Robustness of greenberger–horne–zeilinger and w states for teleportation in external environments, Physics Letters A 375, 922 (2011)

    2011

  201. [209]

    Metwally, Entanglement and quantum teleportation via decohered tripartite entangled states, Annals of Physics 351, 704 (2014)

    N. Metwally, Entanglement and quantum teleportation via decohered tripartite entangled states, Annals of Physics 351, 704 (2014)

    2014

  202. [210]

    M. Chun, Y. Ming, and C. Zhuo-Liang, Controlled quantum teleportation through noisy ghz channel, Communications in Theoretical Physics 53, 489 (2010)

    2010

  203. [211]

    Khan, Entanglement of tripartite states with decoherence in non-inertial frames, Journal of Modern Optics 59, 250 (2012)

    S. Khan, Entanglement of tripartite states with decoherence in non-inertial frames, Journal of Modern Optics 59, 250 (2012)

    2012

  204. [212]

    Zounia, M

    M. Zounia, M. Shamirzaie, and A. Ashouri, Quantum teleportation via noisy bipartite and tripartite accelerating quantum states: beyond the single mode approximation, Journal of Physics A: Mathematical and Theoretical 50, 395302 (2017)

    2017

  205. [213]

    Y.-G. Yang, S. Gao, D. Li, Y.-H. Zhou, and W.-M. Shi, Three-party quantum secret sharing against collective noise, Quantum Information Processing 18, 215 (2019)

    2019

  206. [214]

    Liang, J.-M

    H.-Q. Liang, J.-M. Liu, S.-S. Feng, and J.-G. Chen, Remote state preparation via a ghz-class state in noisy environments, Journal of Physics B: Atomic, Molecular and Optical Physics 44, 115506 (2011)

    2011

  207. [215]

    Liang, J.-M

    H.-Q. Liang, J.-M. Liu, S.-S. Feng, J.-G. Chen, and X.-Y. Xu, Effects of noises on joint remote state preparation via a ghz-class channel, Quantum Information Processing 14, 3857 (2015)

    2015

  208. [216]

    Zhong-Fang, L

    C. Zhong-Fang, L. Jin-Ming, and M. Lei, Deterministic joint remote preparation of an arbitrary two-qubit state in the presence of noise, Chinese Physics B 23, 020312 (2013)

    2013

  209. [217]

    Zhang, M.-q

    C.-y. Zhang, M.-q. Bai, and S.-q. Zhou, Cyclic joint remote state preparation in noisy environment, Quantum Information Processing 17, 146 (2018)

    2018

  210. [218]

    X.-W. Wang, S. Yu, D.-Y. Zhang, and C. Oh, Effect of weak measurement on entanglement distribution over noisy channels, Scientific reports 6, 22408 (2016)

    2016

  211. [219]

    Singh, Arvind, and K

    H. Singh, Arvind, and K. Dorai, Evolution of tripartite entangled states in a decohering environment and their experi- mental protection using dynamical decoupling, Phys. Rev. A 97, 022302 (2018)

    2018

  212. [220]

    Jiang, R.-G

    S.-X. Jiang, R.-G. Zhou, R. Xu, and G. Luo, Cyclic hybrid double-channel quantum communication via bell-state and 27 ghz-state in noisy environments, IEEE Access 7, 80530 (2019)

    2019

  213. [221]

    M. M. Cunha, E. Fonseca, M. Moreno, and F. Parisio, Non-ideal teleportation of tripartite entanglement: Einstein– podolsky–rosen versus greenberger–horne–zeilinger schemes, Quantum Information Processing 16, 254 (2017)

    2017

  214. [222]

    Wang, S.-Q

    X.-W. Wang, S.-Q. Tang, Y. Liu, and J.-B. Yuan, Improving the robustness of entangled states by basis transformation, Entropy 21, 59 (2019)

    2019

  215. [223]

    Gabriel, A

    C. Gabriel, A. Aiello, W. Zhong, T. G. Euser, N. Y. Joly, P. Banzer, M. F¨ ortsch, D. Elser, U. L. Andersen, C. Marquardt, P. S. J. Russell, and G. Leuchs, Entangling different degrees of freedom by quadrature squeezing cylindrically polarized modes, Physical Review Letters 106...

    2011

  216. [224]

    Einstein, B

    A. Einstein, B. Podolsky, and N. Rosen, Can quantum-mechanical description of physical reality be considered complete?, Phys. Rev. 47, 777 (1935)

    1935

  217. [225]

    Hardy, Nonlocality for 2 Particles without Inequalities for Almost-All Entangled States, Physical Review Letters 71, 1665 (1993)

    L. Hardy, Nonlocality for 2 Particles without Inequalities for Almost-All Entangled States, Physical Review Letters 71, 1665 (1993)

    1993

  218. [226]

    T. C. Ralph, S. D. Bartlett, J. L. O’Brien, G. J. Pryde, and H. M. Wiseman, Quantum nondemolition measurements for quantum information, Phys. Rev. A 73, 012113 (2006)

    2006

  219. [227]

    Barbieri, C

    M. Barbieri, C. Cinelli, P. Mataloni, and F. De Martini, Polarization-momentum hyperentangled states: Realization and characterization, Phys. Rev. A 72, 052110 (2005)

    2005

  220. [228]

    Bhatti, J

    D. Bhatti, J. von Zanthier, and G. S. Agarwal, Entanglement of polarization and orbital angular momentum, Phys. Rev. A 91, 062303 (2015). 28 ERRA TUM: TRIP AR TITE ENT ANGLEMENT: FOUNDA TIONS AND APPLICA TIONS On section V, subsection A of this manuscript, we have discussed th...

    2015

Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.