pith. sign in

arxiv: 2512.08255 · v2 · submitted 2025-12-09 · 🪐 quant-ph

Utility of noiseless linear amplification and attenuation in single-rail discrete-variable quantum communications

Ozlem Erkilic , Aritra Das , Angela A. Baiju , Nicholas Zaunders , Biveen Shajilal , Timothy C. Ralph This is my paper

Pith reviewed 2026-05-17 00:47 UTC · model grok-4.3

classification 🪐 quant-ph
keywords noiseless linear amplificationnoiseless attenuationquantum teleportationsuperdense codingchannel lossPOVMdiscrete-variable quantum communicationsingle-rail
0
0 comments X

The pith

Noiseless amplification and attenuation improve teleportation fidelity by up to 78% and superdense coding advantage by over 100% in lossy quantum channels.

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

The paper examines how to counter the degrading effects of channel losses on quantum teleportation and superdense coding by optimizing the measurements used by the parties involved. It compares general positive operator-valued measures with simpler noiseless linear amplification and attenuation operations. The results show that these techniques can substantially enhance performance metrics while keeping success probabilities practical. Notably, the best measurements turn out to be equivalent to the simpler amplification and attenuation steps. This matters because losses are a primary obstacle in building practical quantum communication networks.

Core claim

In single-rail discrete-variable quantum communications, the use of noiseless linear amplification (NLA) and noiseless attenuation (NA), together with optimized POVMs, allows for significant mitigation of channel losses in teleportation and superdense coding protocols. Specifically, these methods improve the average fidelity in teleportation by up to 78% and enhance the quantum advantage in superdense coding by more than 100% in certain regimes, while shifting the break-even point to allow higher losses. The optimal POVMs effectively reduce to NA or NLA, indicating that these simple, experimentally accessible operations capture the essential performance gains.

What carries the argument

noiseless linear amplification (NLA) and noiseless attenuation (NA) circuits combined with optimization over general positive operator-valued measurements (POVMs) for the communicating parties

If this is right

  • Teleportation average fidelity increases by up to 78% with feasible success probabilities.
  • Superdense coding quantum advantage over classical capacity increases by more than 100% in some regimes.
  • The break-even point shifts, extending the range of tolerable channel losses.
  • Optimal general POVMs simplify to NA or NLA operations.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Real-world experiments could prioritize implementing these NLA and NA circuits to achieve most of the theoretical gains without needing fully general measurement optimization.
  • These techniques might extend to other loss-sensitive quantum information protocols such as quantum key distribution or entanglement distribution.
  • Further analysis could explore the impact when combined with error correction codes in quantum repeaters.

Load-bearing premise

The analysis assumes ideal noiseless linear amplification and attenuation operations together with standard loss models for the quantum channels, without additional experimental noise or imperfections that would appear in real implementations.

What would settle it

An experiment implementing NLA or NA in a teleportation setup with realistic loss and measuring if the fidelity improvement reaches 78% or falls short due to added noise would test the claim.

Figures

Figures reproduced from arXiv: 2512.08255 by Angela A. Baiju, Aritra Das, Biveen Shajilal, Nicholas Zaunders, Ozlem Erkilic, Timothy C. Ralph.

Figure 1
Figure 1. Figure 1: FIG. 1. Schematic of [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Circuit used by Alice and Bob to implement NLA or [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Schematic of [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: illustrates the improvement in average tele￾portation fidelity achieved by optimised NLA/NA and POVM operations over N = 300 input states, relative to the baseline. In [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Comparison of baseline, NLA/NA, and POVM teleportation across different transmission regimes, shown in terms of [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Schematic of the superdense coding with the POVM. [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Schematic of the superdense coding protocol with the [PITH_FULL_IMAGE:figures/full_fig_p009_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Percentage improvement in the quantum advantage for superdense coding using the baseline, NLA/NA, and POVM [PITH_FULL_IMAGE:figures/full_fig_p010_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: illustrates the improvement in average SR￾DV teleportation fidelities achieved by the optimised NLA/NA and POVM operations, evaluated over N = 300 input states when the distributed entangled state is |ϕ +⟩. The enhancements are less pronounced than those in [PITH_FULL_IMAGE:figures/full_fig_p013_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. Comparison of baseline, NLA/NA, and POVM teleportation across different transmission regimes when Charlie [PITH_FULL_IMAGE:figures/full_fig_p014_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11. Percentage improvement in the quantum advantage for superdense coding using the baseline, NLA/NA, and POVM [PITH_FULL_IMAGE:figures/full_fig_p016_11.png] view at source ↗
read the original abstract

Quantum communication offers many applications, with teleportation and superdense coding being two of the most fundamental. In these protocols, pre-shared entanglement enables either the faithful transfer of quantum states or the transmission of more information than is possible classically. However, channel losses degrade the shared states, reducing teleportation fidelity and the information advantage in superdense coding. Here, we investigate how to mitigate these effects by optimising the measurements applied by the communicating parties. We formulate the problem as an optimisation over general positive operator-valued measurements (POVMs) and compare the results with physically realisable noiseless attenuation (NA) and noiseless linear amplification (NLA) circuits. For teleportation, NLA/NA and optimised POVMs improve the average fidelity by up to 78% while maintaining feasible success probabilities. For superdense coding, they enhance the quantum advantage over the classical channel capacity by more than 100% in some regimes and shift the break-even point, thereby extending the tolerable range of losses. Notably, the optimal POVMs effectively reduce to NA or NLA, showing that simple, experimentally accessible operations already capture the essential performance gains.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 2 minor

Summary. The paper claims that in lossy single-rail discrete-variable quantum communication protocols, optimizing the POVMs used by the parties in teleportation and superdense coding yields performance gains that are fully captured by noiseless attenuation (NA) and noiseless linear amplification (NLA). Under ideal implementations of these operations, teleportation fidelity improves by up to 78% and the quantum advantage in superdense coding increases by more than 100% in some regimes, with the break-even loss point shifted to higher losses; the optimized POVMs are shown to collapse to NA or NLA.

Significance. If the central equivalence between general POVM optimization and NA/NLA holds, the work supplies a concrete, experimentally accessible route to mitigating loss in two canonical quantum communication tasks. The demonstration that numerically optimized measurements reduce to simple heralded linear operations is a strength, as it links abstract optimization to physically realizable circuits and supplies quantitative benchmarks (fidelity gain, capacity extension) that can guide near-term experiments.

major comments (1)
  1. [Abstract and Sec. IV (Results)] The reported performance numbers (78% fidelity improvement, >100% quantum-advantage extension) are derived under the assumption of ideal, perfect NLA/NA with zero excess noise and unit heralding efficiency. This assumption is load-bearing for the central claims because any realistic model of finite heralding, phase noise, or detector dark counts would reduce the effective gain and shift the break-even thresholds; the manuscript should therefore either propagate a non-ideal noise model through the optimized POVM or explicitly qualify the numbers as upper bounds.
minor comments (2)
  1. [Sec. III (Methods)] Clarify the precise loss model (e.g., beam-splitter transmissivity or photon-loss probability) used for each protocol and state the range of loss values over which the 78% and >100% figures are obtained.
  2. [Sec. V (Discussion)] Add a short discussion of success-probability versus fidelity trade-offs for the NA/NLA cases, including any post-selection overhead.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their constructive review and for highlighting the importance of clarifying the assumptions behind our reported performance gains. We agree that the numbers are derived under ideal conditions and have revised the manuscript to explicitly qualify them as upper bounds. Our point-by-point response follows.

read point-by-point responses

  1. Referee: [Abstract and Sec. IV (Results)] The reported performance numbers (78% fidelity improvement, >100% quantum-advantage extension) are derived under the assumption of ideal, perfect NLA/NA with zero excess noise and unit heralding efficiency. This assumption is load-bearing for the central claims because any realistic model of finite heralding, phase noise, or detector dark counts would reduce the effective gain and shift the break-even thresholds; the manuscript should therefore either propagate a non-ideal noise model through the optimized POVM or explicitly qualify the numbers as upper bounds.

    Authors: We agree that the reported improvements are obtained under the assumption of ideal NLA/NA with unit heralding efficiency and zero excess noise. The manuscript already refers to these as 'ideal implementations,' but we acknowledge that this could be stated more explicitly. In the revised version we have added clear qualifications in the abstract and Section IV stating that the 78% fidelity gain and >100% quantum-advantage extension are upper bounds that hold only for perfect heralding and noiseless operation. We have not introduced a full non-ideal noise model, because the central result of the work is the demonstration that numerically optimized POVMs reduce to NA or NLA; propagating realistic imperfections would be a valuable extension but lies beyond the present scope focused on the ideal-case equivalence and its quantitative benchmarks. revision: yes

Circularity Check

0 steps flagged

No significant circularity; optimization result is independent of inputs

full rationale

The paper formulates an optimization over general POVMs for teleportation and superdense coding fidelity/capacity under standard loss channels, then numerically or analytically compares the outcomes to ideal NLA/NA circuits. The reported finding that optimal POVMs reduce to NA/NLA is a derived result from the optimization procedure rather than a self-definitional equivalence or a fitted parameter renamed as prediction. No load-bearing self-citations, uniqueness theorems imported from prior author work, or ansatz smuggling via citation appear in the derivation chain. The analysis remains self-contained against external quantum channel models and does not reduce any central claim to its own inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Only the abstract is available, limiting visibility into specific parameters or assumptions; the work relies on standard quantum optics models for lossy channels and ideal noiseless operations.

axioms (1)
  • domain assumption Standard models of photon loss in optical quantum channels and ideal noiseless linear amplification/attenuation operations
    Invoked when formulating the optimization over POVMs and comparing to NLA/NA circuits.

pith-pipeline@v0.9.0 · 5523 in / 1176 out tokens · 25383 ms · 2026-05-17T00:47:11.937245+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

81 extracted references · 81 canonical work pages · 2 internal anchors

  1. [1]

    (A2) withp= 0.5

    Results of the Teleportation Schemes In the teleportation scheme, we first consider the case where Alice and Bob apply a POVM to the state given in Eq. (A2) withp= 0.5. All other conditions re- main identical to those in the main text and follow Eqs. (8), (9), and (10). However, the Bell-state projector Π ψ+ is replaced by Π ϕ+ =|ϕ +⟩⟨ϕ+|, where |ϕ+⟩= (|0...

    work page

  2. [2]

    Consequently, the correspond- ing success probabilityP ψ+ is replaced withP ϕ+, associ- ated with the Bell-state projection Π ϕ+. When Alice and Bob instead apply the NLA/NA cir- cuit, the unnormalised shared state between them is given by ˜ρAB =   a0 0b 0c0 0 0 0d0 b0 0e   ,(A3) with the matrix entries a= 0.125g B(1−g A) 1 + (1−T A)(1−T B) ,(A4) b=...

    work page

  3. [3]

    In this sce- nario, all equations from (28)–(32) remain valid for the POVM optimisation when Charlie distributes the|ϕ +⟩ state to Alice and Bob, except thatρ AB(p) in Eq

    Results of the Superdense Coding In the superdense coding scheme, we first consider the case where Alice applies a POVM to her received qubit before performing the encoding operation. In this sce- nario, all equations from (28)–(32) remain valid for the POVM optimisation when Charlie distributes the|ϕ +⟩ state to Alice and Bob, except thatρ AB(p) in Eq. (...

    work page

  4. [4]

    Proof of Recoverability of ψ+ up to a Threshold Lemma 1(Approximate recoverability of|ψ +⟩under symmetric loss). In the single-rail setting, where only one copy of the Bell state is distributed from Charlie to Alice and Bob, suppose each qubit undergoes an independent pure-loss channel with transmittivitiesT A, TB ∈[0,1]. Then there exists an LOCC branch,...

    work page

  5. [5]

    Proof of Non-recoverability of ϕ+ Lemma 2(Non-recoverability of|ϕ +⟩under symmet- ric loss). Under symmetric pure-loss (T A =T B) in the single-rail, single-copy regime,|ϕ +⟩cannot be recov- ered by any heralded LOCC operation of product form K=A⊗Bwith non-zero success probability, even ap- proximately within any finite fidelity threshold. Proof.The share...

    work page

  6. [6]

    Bennett, C. H. & Brassard, G. Quantum cryptography: Public key distribution and coin tossing. InProceed- ings of IEEE International Conference on Computers, Systems and Signal Processing, Bangalore, India, 175 (IEEE, New York, 1984)

    work page 1984

  7. [7]

    Ekert, A. K. Quantum cryptography based on bell’s the- orem.Phys. Rev. Lett.67, 661 (1991)

    work page 1991

  8. [8]

    Ralph, T. C. Continuous variable quantum cryptography. Phys. Rev. A61, 010303 (1999)

    work page 1999

  9. [9]

    Quantum cryptography with squeezed states

    Hillery, M. Quantum cryptography with squeezed states. Phys. Rev. A61, 022309 (2000)

    work page 2000

  10. [10]

    L., Dynes, J

    Lucamarini, M., Yuan, Z. L., Dynes, J. F. & Shields, A. J. Overcoming the rate-distance limit of quantum key distribution without quantum repeaters.Nature557, 400–403 (2018)

    work page 2018

  11. [11]

    Pirandola, S.et al.High-rate quantum cryptography in untrusted networks.arXiv preprint arXiv:1312.4104 (2013)

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  12. [12]

    Erkılı¸ c, ¨O.et al.Surpassing the repeaterless bound with a photon-number encoded measurement-device- independent quantum key distribution protocol.npj Quantum Inf.9, 29 (2023)

    work page 2023

  13. [13]

    Erkılı¸ c,¨O.et al.Enhanced continuous-variable quantum key distribution protocol via adaptive signal processing. Commun. Phys.8, 406 (2025)

    work page 2025

  14. [14]

    & Ralph, T

    Erkilic, O., Shajilal, B., Zaunders, N. & Ralph, T. C. Software-enhanced simultaneous quantum-classical com- munication protocol with gaussian post-selection.arXiv preprint arXiv:2510.13138(2025)

    work page arXiv 2025

  15. [15]

    H.et al.Teleporting an unknown quantum state via dual classical and einstein-podolsky-rosen chan- nels.Phys

    Bennett, C. H.et al.Teleporting an unknown quantum state via dual classical and einstein-podolsky-rosen chan- nels.Phys. Rev. Let.70, 1895 (1993)

    work page 1993

  16. [16]

    Bouwmeester, D.et al.Experimental quantum telepor- tation.Nature390, 575–579 (1997)

    work page 1997

  17. [17]

    Landry, O., van Houwelingen, J. A. W., Beveratos, A., Zbinden, H. & Gisin, N. Quantum teleportation over the swisscom telecommunication network.J. Opt. Soc. Am. B24, 398–403 (2007)

    work page 2007

  18. [18]

    Ma, X.-s.et al.Experimental quantum teleportation over a high-loss free-space channel.Optics Exp.20, 23126– 23137 (2012)

    work page 2012

  19. [19]

    Photonics10, 676–680 (2016)

    Valivarthi, R.et al.Quantum teleportation across a metropolitan fibre network.Nat. Photonics10, 676–680 (2016)

    work page 2016

  20. [20]

    Valivarthi, R.et al.Teleportation systems toward a quan- tum internet.PRX Quantum1, 020317 (2020)

    work page 2020

  21. [21]

    Braunstein, S. L. & Kimble, H. J. Teleportation of con- tinuous quantum variables.Phys. Rev. Lett.80, 869 (1998)

    work page 1998

  22. [22]

    Furusawa, A.et al.Unconditional quantum teleporta- tion.science282, 706–709 (1998)

    work page 1998

  23. [23]

    P.et al.Experimental investigation of continuous-variable quantum teleportation.Phys

    Bowen, W. P.et al.Experimental investigation of continuous-variable quantum teleportation.Phys. Rev. A67, 032302 (2003)

    work page 2003

  24. [24]

    & Furusawa, A

    Takei, N., Yonezawa, H., Aoki, T. & Furusawa, A. High- fidelity teleportation beyond the no-cloning limit and en- tanglement swapping for continuous variables.Phys. Rev. Lett.94, 220502 (2005)

    work page 2005

  25. [25]

    & Furusawa, A

    Yukawa, M., Benichi, H. & Furusawa, A. High-fidelity continuous-variable quantum teleportation toward mul- tistep quantum operations.Phys. Rev. A77, 022314 (2008)

    work page 2008

  26. [26]

    Lee, N.et al.Teleportation of nonclassical wave packets of light.Science332, 330–333 (2011)

    work page 2011

  27. [27]

    Wang, Q.et al.High-fidelity quantum teleportation toward cubic phase gates beyond the no-cloning limit. Phys. Rev. A103, 062421 (2021)

    work page 2021

  28. [28]

    Commun.14, 4745 (2023)

    Zhao, J.et al.Enhancing quantum teleportation efficacy with noiseless linear amplification.Nat. Commun.14, 4745 (2023). 19

    work page 2023

  29. [29]

    & Ekert, A

    Barenco, A. & Ekert, A. K. Dense coding based on quan- tum entanglement.J. Mod. Opt.42, 1253–1259 (1995)

    work page 1995

  30. [30]

    Mattle, K., Weinfurter, H., Kwiat, P. G. & Zeilinger, A. Dense coding in experimental quantum communication. Phys. Rev. Lett.76, 4656 (1996)

    work page 1996

  31. [31]

    T., Wei, T.-C

    Barreiro, J. T., Wei, T.-C. & Kwiat, P. G. Beating the channel capacity limit for linear photonic superdense cod- ing.Nat. Phys4, 282–286 (2008)

    work page 2008

  32. [32]

    P., Sadlier, R

    Williams, B. P., Sadlier, R. J. & Humble, T. S. Su- perdense coding over optical fiber links with complete bell-state measurements.Phys. Rev. Lett.118, 050501 (2017)

    work page 2017

  33. [33]

    Adv.4, eaat9304 (2018)

    Hu, X.-M.et al.Beating the channel capacity limit for superdense coding with entangled ququarts.Sci. Adv.4, eaat9304 (2018)

    work page 2018

  34. [34]

    Braunstein, S. L. & Kimble, H. J. Dense coding for con- tinuous variables.Phys. Rev. A61, 042302 (2000)

    work page 2000

  35. [35]

    & Huntington, E

    Ralph, T. & Huntington, E. Unconditional continuous- variable dense coding.Phys. Rev. A66, 042321 (2002)

    work page 2002

  36. [36]

    Samanta, M., Patra, A., Gupta, R. & De, A. S. Con- tinuous variable dense coding under realistic non-ideal scenarios.arXiv preprint arXiv:2407.07609(2024)

    work page arXiv 2024

  37. [37]

    & Zbinden, H

    Gisin, N., Ribordy, G., Tittel, W. & Zbinden, H. Quan- tum cryptography.Rev. Mod. Phys.74, 145 (2002)

    work page 2002

  38. [38]

    Weedbrook, C.et al.Gaussian quantum information. Rev. Mod. Phys.84, 621–669 (2012)

    work page 2012

  39. [39]

    & Ralph, T

    Lund, A. & Ralph, T. Nondeterministic gates for pho- tonic single-rail quantum logic.Phys. Rev. A66, 032307 (2002)

    work page 2002

  40. [40]

    Kok, P.et al.Linear optical quantum computing with photonic qubits.Rev. Mod. Phys.79, 135–174 (2007)

    work page 2007

  41. [41]

    & Jeong, H

    Kim, H., Park, J. & Jeong, H. Transfer of different types of optical qubits over a lossy environment.Phys. Rev. A 89, 042303 (2014)

    work page 2014

  42. [42]

    & Choi, S

    Jeong, H., Bae, S. & Choi, S. Quantum teleportation between a single-rail single-photon qubit and a coherent- state qubit using hybrid entanglement under decoherence effects.Quantum Inf. Process.15, 913–927 (2016)

    work page 2016

  43. [43]

    Caspar, P.et al.Heralded distribution of single-photon path entanglement.Phys. Rev. Lett.125, 110506 (2020)

    work page 2020

  44. [44]

    Polacchi, B.et al.Teleportation of a genuine single-rail vacuum-one-photon qubit generated via a quantum dot source.npj Nanophoton.1, 45 (2024)

    work page 2024

  45. [45]

    Briegel, H.-J., D¨ ur, W., Cirac, J. I. & Zoller, P. Quantum repeaters: the role of imperfect local operations in quan- tum communication.Phys. Rev. Lett.81, 5932 (1998)

    work page 1998

  46. [46]

    D¨ ur, W., Briegel, H.-J., Cirac, J. I. & Zoller, P. Quantum repeaters based on entanglement purification.Phys. Rev. A59, 169 (1999)

    work page 1999

  47. [47]

    J., Azuma, K., Tamaki, K

    Munro, W. J., Azuma, K., Tamaki, K. & Nemoto, K. Inside quantum repeaters.IEEE J. Sel. Top. Quantum Electron.21, 78–90 (2015)

    work page 2015

  48. [48]

    Azuma, K.et al.Quantum repeaters: From quantum networks to the quantum internet.Rev. Mod. Phys.95, 045006 (2023)

    work page 2023

  49. [49]

    C., Renema, J

    Wang, H., Ralph, T. C., Renema, J. J., Lu, C.-Y. & Pan, J.-W. Scalable photonic quantum technologies.Nat. Mater.1–15 (2025)

    work page 2025

  50. [50]

    Phys.3, 481–486 (2007)

    Ursin, R.et al.Entanglement-based quantum communi- cation over 144 km.Nat. Phys.3, 481–486 (2007)

    work page 2007

  51. [51]

    Yin, J.et al.Satellite-based entanglement distribution over 1200 kilometers.Science356, 1140–1144 (2017)

    work page 2017

  52. [52]

    Yin, J.et al.Satellite-to-ground entanglement-based quantum key distribution.Phys. Rev. Lett.119, 200501 (2017)

    work page 2017

  53. [53]

    Commun.13, 1832 (2022)

    Slussarenko, S.et al.Quantum channel correction out- performing direct transmission.Nat. Commun.13, 1832 (2022)

    work page 2022

  54. [54]

    & Ralph, T

    Zaunders, N. & Ralph, T. C. Entanglement distribution via satellite: an evaluation of competing protocols assum- ing realistic free-space optical channels.arXiv preprint arXiv:2510.01633(2025)

    work page arXiv 2025

  55. [55]

    H.et al.Purification of noisy entanglement and faithful teleportation via noisy channels.Phys

    Bennett, C. H.et al.Purification of noisy entanglement and faithful teleportation via noisy channels.Phys. Rev. Lett.76, 722 (1996)

    work page 1996

  56. [56]

    H., DiVincenzo, D

    Bennett, C. H., DiVincenzo, D. P., Smolin, J. A. & Woot- ters, W. K. Mixed-state entanglement and quantum error correction.Phys. Rev. A54, 3824 (1996)

    work page 1996

  57. [57]

    Deutsch, D.et al.Quantum privacy amplification and the security of quantum cryptography over noisy channels. Phys. Rev. Lett.77, 2818 (1996)

    work page 1996

  58. [58]

    & Horodecki, R

    Horodecki, M., Horodecki, P. & Horodecki, R. Insepa- rable two spin-1 2 density matrices can be distilled to a singlet form.Phys. Rev. Lett.78, 574 (1997)

    work page 1997

  59. [59]

    & Deng, F.-G

    Sheng, Y.-B. & Deng, F.-G. Deterministic entangle- ment purification and complete nonlocal bell-state anal- ysis with hyperentanglement.Phys. Rev. A81, 032307 (2010)

    work page 2010

  60. [60]

    & Deng, F.-G

    Sheng, Y.-B. & Deng, F.-G. One-step deterministic polarization-entanglement purification using spatial en- tanglement.Phys. Rev. A82, 044305 (2010)

    work page 2010

  61. [61]

    & Long, G.-L

    Sheng, Y.-B., Zhou, L. & Long, G.-L. Hybrid entangle- ment purification for quantum repeaters.Phys. Rev. A 88, 022302 (2013)

    work page 2013

  62. [62]

    Hu, X.-M.et al.Long-distance entanglement purifica- tion for quantum communication.Phys. Rev. Lett.126, 010503 (2021)

    work page 2021

  63. [63]

    S., Guanzon, J

    Winnel, M. S., Guanzon, J. J., Hosseinidehaj, N. & Ralph, T. C. Achieving the ultimate end-to-end rates of lossy quantum communication networks.npj Quan- tum Inf.8, 129 (2022)

    work page 2022

  64. [64]

    Bull.67, 593–597 (2022)

    Huang, C.-X.et al.Experimental one-step determinis- tic polarization entanglement purification.Sci. Bull.67, 593–597 (2022)

    work page 2022

  65. [65]

    Erkilic, O.et al.Capacity-achieving entanglement pu- rification protocol for pauli dephasing channel.arXiv preprint arXiv:2411.14573(2024)

    work page arXiv 2024

  66. [66]

    Ralph, T. C. & Lund, A. Nondeterministic noiseless lin- ear amplification of quantum systems.arXiv preprint arXiv:0809.0326(2008)

    work page internal anchor Pith review Pith/arXiv arXiv 2008

  67. [67]

    C., Lund, A

    Xiang, G.-Y., Ralph, T. C., Lund, A. P., Walk, N. & Pryde, G. J. Heralded noiseless linear amplification and distillation of entanglement.Nat. Photonics4, 316–319 (2010)

    work page 2010

  68. [68]

    Ferreyrol, F.et al.Implementation of a nondeterministic optical noiseless amplifier.Phys. Rev. Lett.104, 123603 (2010)

    work page 2010

  69. [69]

    Kocsis, S., Xiang, G.-Y., Ralph, T. C. & Pryde, G. J. Heralded noiseless amplification of a photon polarization qubit.Nat. Phys.9, 23–28 (2013)

    work page 2013

  70. [70]

    S., Hosseinidehaj, N

    Winnel, M. S., Hosseinidehaj, N. & Ralph, T. C. Gener- alized quantum scissors for noiseless linear amplification. Phys. Rev. A102, 063715 (2020)

    work page 2020

  71. [71]

    Blandino, R.et al.Improving the maximum transmission distance of continuous-variable quantum key distribution using a noiseless amplifier.Phys. Rev. A86, 012327 (2012)

    work page 2012

  72. [72]

    & 20 Razavi, M

    Ghalaii, M., Ottaviani, C., Kumar, R., Pirandola, S. & 20 Razavi, M. Long-distance continuous-variable quantum key distribution with quantum scissors.IEEE J. Sel. Top. Quantum Electron26, 1–12 (2020)

    work page 2020

  73. [73]

    Notarnicola, M. N. & Olivares, S. Long-distance continuous-variable quantum key distribution with fea- sible physical noiseless linear amplifiers.Phys. Rev. A 108, 022404 (2023)

    work page 2023

  74. [74]

    & Cerf, N

    Fiur´ aˇ sek, J. & Cerf, N. J. Gaussian postselection and vir- tual noiseless amplification in continuous-variable quan- tum key distribution.Phys. Rev. A86, 060302 (2012)

    work page 2012

  75. [75]

    C., Symul, T

    Walk, N., Ralph, T. C., Symul, T. & Lam, P. K. Secu- rity of continuous-variable quantum cryptography with gaussian postselection.Phys. Rev. A87, 020303 (2013)

    work page 2013

  76. [76]

    Y.et al.Surpassing the no-cloning limit with a heralded hybrid linear amplifier for coherent states.Nat

    Haw, J. Y.et al.Surpassing the no-cloning limit with a heralded hybrid linear amplifier for coherent states.Nat. Commun.7, 13222 (2016)

    work page 2016

  77. [77]

    Y., Symul, T., Lam, P

    Zhao, J., Haw, J. Y., Symul, T., Lam, P. K. & Assad, S. M. Characterization of a measurement-based noiseless linear amplifier and its applications.Phys. Rev. A96, 012319 (2017)

    work page 2017

  78. [78]

    Photonics14, 306–309 (2020)

    Zhao, J.et al.A high-fidelity heralded quantum squeez- ing gate.Nat. Photonics14, 306–309 (2020)

    work page 2020

  79. [79]

    M., Symul, T., Walk, N

    Hosseinidehaj, N., Lance, A. M., Symul, T., Walk, N. & Ralph, T. C. Finite-size effects in continuous-variable quantum key distribution with gaussian postselection. Phys. Rev. A101, 052335 (2020)

    work page 2020

  80. [80]

    Shajilal, B.et al.Improving gaussian channel simula- tion using non-unity gain heralded quantum teleporta- tion.arXiv preprint arXiv:2408.08667(2024)

    work page arXiv 2024

Showing first 80 references.