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REVIEW 3 major objections 4 minor 30 references

A state’s second moments form a two-dimensional purity-budget plane where crossing the classical envelope certifies NPT entanglement, using only n+1 purity measurements.

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2026-08-02 19:00 UTC pith:5SWVN7AB

load-bearing objection Two-qubit purity-budget bounds check out and the fixed-purity magic ceilings are new, but the dimension-agnostic NPT certification claim is carried by an unproved bridge lemma that the paper's own examples contradict. the 3 major comments →

arxiv 2603.03887 v2 pith:5SWVN7AB submitted 2026-03-04 quant-ph

Kinematic budget of quantum correlations

Maaz Khan , Subhadip Mitra This is my paper
classification quant-ph
keywords purity budgetquantum correlationsNPT entanglemententanglement witnesssteeringBell nonlocalitystabiliser magictime-reversal symmetry
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

This paper claims that at the level of observable second moments—the quantities that define purity—all types of quantum correlation collapse into a single geometric picture. A state’s total purity budget splits into a local part (subsystem polarizations) and a nonlocal part (correlations), yielding a compact plane where physical states occupy a hole-free region bounded by purity and time-reversal overlap. Crossing the classical envelope in this plane must activate time-odd, asymmetric generators, which the paper argues necessarily produce negative eigenvalues under partial transpose—a basis-independent entanglement witness. For two qubits the boundaries are analytic: a single curve isolates classical correlations while nested regions define steering, Bell nonlocality, absolute separability, and caps on non-stabiliser magic. The payoff is that certifying these resources requires only n+1 purity measurements, with sample complexity independent of Hilbert space dimension.

Core claim

Every n-partite state projects onto a compact 2D plane via the split of purity into local (BL) and nonlocal (BNL) second-moment budgets. The paper’s central claim: crossing the “classical envelope” in this plane forces the activation of time-odd generator sectors, which—because local time reversal equals partial transposition—guarantees a negative eigenvalue under PT. Thus any excursion above the envelope is a basis-independent NPT entanglement witness. For two qubits the boundaries are analytic: one curve gives the threshold for entanglement and steering, another guarantees CHSH violation, and R = 1/3 marks absolute separability. Beyond two qubits, nested QC envelopes certify biseparable an

What carries the argument

The purity budget: for an n-partite state with total dimension D, the total second-moment budget B = D·P − 1 splits into local (BL) and nonlocal (BNL) contributions, with rationalized coordinates X = sqrt(BL/((D−1)P)) and Y = sqrt(BNL/((D−1)P)). The classical envelope (C) is the maximum BNL achievable with time-symmetric (diagonal/real-symmetric) generators; nested QC(m, n−m) envelopes are its refinements. The load-bearing identity is that local time reversal in the LU-invariant frame is partial transposition, so states above an envelope carry irreducible time-odd A-sector generators that force negative PT eigenvalues.

Load-bearing premise

The load-bearing premise is the unproven bridge lemma that an “irreducible” presence of time-odd generators, said to be forced by crossing the envelope, necessarily yields a negative eigenvalue under partial transposition; the paper’s own example of a pure product state containing σy⊗σy yet being PPT shows time-odd generators alone are not sufficient, and “irreducible” is left undefined.

What would settle it

A single state in 2⊗3 or 3⊗3 with nonnegative partial transpose and nonlocal budget above the classical/QC envelope would refute the general guarantee; a two-qubit state with BNL > 1 and zero negativity would refute the analytic two-qubit claim. Such a search can be carried out numerically by sampling random states and checking the budget coordinates against the envelope.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • A two-qubit state with BNL > 1 is necessarily entangled and steerable; BNL > 3/2 additionally guarantees a CHSH Bell violation.
  • The absolute separability boundary R = 1/3 means every state below it is separable, and the maximum negativity is bounded by a function of R alone.
  • For n-partite systems, crossing the outermost QC envelope certifies genuine multipartite NPT entanglement; intermediate envelopes certify entanglement across at least m+1 subsystems.
  • Locating a state and certifying these resources requires only n+1 purity measurements (one global, n marginals), with O(1/ε²) sample complexity independent of Hilbert space dimension.
  • Noise dynamics become constrained flows in the (X,Y) plane: local noise degrades correlations, correlated noise can redistribute the budget, and natural decoherence obeys an empirical no-go rule that P and Q cannot both increase.

Where Pith is reading between the lines

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

  • If the bridge lemma holds, the same budget map could serve as a routine layer for current quantum hardware diagnostics, since purity estimates from two-copy or randomized measurements are already practical.
  • The framework suggests a systematic way to search for new entanglement witnesses: any basis-independent quadratic functional of the state that lies above the QC envelope should certify NPT entanglement—a conjecture only partially covered by the paper’s examples.
  • The time-reversal/PT equivalence is tied to local unitary invariance; extending the geometry to systems with superselection rules or fermionic parity would likely require a refined algebraic mapping.
  • The empirical no-go rule (natural dynamics cannot increase P and Q simultaneously) resembles a macroscopic second-law for correlation resources; deriving it from Markovianity or detailed balance is not addressed in the paper.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 4 minor

Summary. The paper proposes a local-unitary-invariant 'purity budget' (global and marginal purities) that projects any multipartite state onto a two-dimensional (X,Y) plane, with B_L and B_NL measuring local and nonlocal second-moment content. The central claim is that the feasible region is hole-free, bounded by classical (C) and quantum-classical (QC) envelopes, and that any excursion above an envelope forces the activation of 'time-odd' generators, guaranteeing NPT entanglement in arbitrary dimensions from only n+1 purity measurements. For two qubits, the paper derives exact thresholds for the classical envelope, entanglement, steering, CHSH nonlocality, geometric discord, negativity, and stabilizer Rényi-2 magic, and it illustrates decoherence as flows in this plane. The two-qubit analytic results are mostly elementary and correct, but the universal dimension-agnostic certification claim rests on unproved and, as stated, false bridging assertions.

Significance. If the general NPT-certification claim were established, the paper would be highly significant: it would provide a basis-independent, dimension-independent entanglement witness requiring only global and marginal purities, unifying discord, entanglement, steering, Bell nonlocality, and magic in a single kinematic diagram. The two-qubit sections contain genuinely checkable results: B_NL > 1 is a valid entanglement/steering witness for two-qubit states, the R ≤ 1/3 absolute separability threshold matches Gurvits-Barnum, and the negativity and CHSH bounds are derived cleanly. However, the two-qubit results are not sufficient to support the paper's headline claims. The general bridge from envelope crossing to NPT is asserted rather than proved, and the provided justification is contradicted by elementary PPT states containing time-odd generators. The paper's value is therefore conditional on a missing proof that is not supplied.

major comments (3)
  1. [Methods: 'The QC envelopes'] The entire dimension-agnostic NPT-certification claim rests on the sentence: 'Because the A-sector generators are time-odd, their irreducible presence manifests through negative eigenvalues under PT.' This is asserted without proof, and as stated it is false: the pure product state |+i><+i| ⊗ |+i><+i| contains the time-odd A generator σ_y⊗σ_y in its expansion (Eq. (1)) yet is separable and PPT. The qualifier 'irreducible' is never defined, so no criterion is given that would exclude this state while applying to states above the envelope. The two-qubit case is saved only by the independent direct bound B_NL ≤ 1 for separable states, which is not the argument used and does not extend to 2⊗3, 3⊗3, or n-qubit systems. Thus the headline guarantee of NPT entanglement from n+1 purity measurements is unsupported.
  2. [Methods: 'The QC envelopes', steps 1–4] The convex-hull algorithm for the QC envelopes is justified only by the paragraph 'It is not difficult to see why this algorithm works.' No proof is given that the listed V_pure, V_cor, and V_hinge points attain the maximum B_NL for each B_L over all Q_m C_{n−m} states. The observation that real symmetric generators can be locally rotated to diagonal form addresses a state-wise canonical form, not the global optimization over mixtures and marginal-purity constraints. Since the envelope is precisely the capacity whose crossing is claimed to force NPT, the unproven optimality of this envelope is load-bearing.
  3. [Methods: 'Feasible and experimentally accessible'; Conclusion] The hole-free completeness of the (X,Y) projection for arbitrary dimensions is argued from continuity of the quadratic map to the budget components. A continuous image of a connected or simply connected domain need not be simply connected, so this topological argument is invalid. For two qubits the explicit parametrization (7)–(8) may establish the claim, but no analogous construction is supplied for higher-dimensional systems. Consequently the assertion that P and Q completely determine the feasible region—and hence that n+1 purity measurements locate a state relative to all resource boundaries—is not established beyond two qubits.
minor comments (4)
  1. [Kinematic bounds on quantum magic] The statement that 'for two-qubit systems, there is a state with nonzero magic for every point beyond the C envelope' is not proved. The preceding argument only shows that rank-one correlation matrices eliminate magic; it does not construct a magic state at every point above the envelope.
  2. [Operational impact: Decoherence as budget flow] The 'empirical arrow of decoherence' (P and Q cannot increase simultaneously) is presented as a general rule but is only illustrated for specific channels. The text itself calls it empirical, yet the caption of Fig. 5 and Table I state it as a universal no-go rule; this overstates the evidence.
  3. [Supplementary Information, Ref. [3]] The Schrödinger reference is dated 2008 with pages 446–452; the original paper is 1935, pages 446–451. Please correct the bibliographic data.
  4. [Fig. 1 caption] The caption labels both a 'Classical envelope' and a 'Separable boundary'. The text says these coincide for two qubits, but the figure shows distinct curves. Clarify which curve is the R=1/3 absolute separability limit and which is the B_NL=1 envelope.

Circularity Check

0 steps flagged

No circularity: the two-qubit results are independently checkable and no fitted parameter is relabeled as a prediction; the n-partite NPT guarantee rests on an unproved bridge, but that is a proof gap, not a circular reduction.

full rationale

The paper's derivation chain does not exhibit a step in which an output is equal to an input by construction. The two-qubit C envelope (BNL = 1) is obtained by maximizing the nonlocal budget over states with diagonal classical correlations, and the claim that BNL > 1 witnesses entanglement and steering is independently verifiable: for separable two-qubit states the correlation matrix is a convex combination of rank-one outer products, so the Frobenius norm is at most 1 by the triangle inequality. No parameter is fitted to the target conclusion, and the sample-complexity statement is a standard consequence of purity estimation via SWAP tests or classical shadows. The main concern is the dimension-agnostic NPT-certification proof in Methods, specifically the sentence: Because the A-sector generators are time-odd, their irreducible presence manifests through negative eigenvalues under PT. This step is asserted without derivation and, taken literally, is contradicted by pure product states that contain sigma_y tensor sigma_y yet are PPT. This is a serious unproved lemma in the general NPT claim, and the convex-hull envelope algorithm is also justified only heuristically. However, these are correctness/rigor gaps, not circularity: time-odd is not defined as PT-negative, the envelopes are not defined as the PPT boundary, and the argument does not reduce to renaming a fitted quantity. There are no load-bearing self-citations and no imported uniqueness theorem from the authors' prior work. Accordingly, the circularity score is 0.

Axiom & Free-Parameter Ledger

0 free parameters · 9 axioms · 0 invented entities

The ledger is clean of fitted parameters — the paper's strength — and introduces no exotic entities: the H⊕S⊕A time-symmetry split is standard Lie-algebra structure. The cost is concentrated in four unproven structural assumptions (A-sector-to-PT lemma, envelope optimality, hole-free completeness, PT/time-reversal identification) that collectively carry the general n-partite headline claim.

axioms (9)
  • standard math Peres-Horodecki criterion: two-qubit entanglement is equivalent to NPT.
    Used throughout the two-qubit section to equate C-envelope crossings with entanglement.
  • standard math Horodecki et al. CHSH condition: two-qubit CHSH violation iff t_p^2 + t_q^2 > 1.
    Basis for the guaranteed-violation and possibility regions in Fig. 1.
  • standard math Gurvits-Barnum largest separable ball: states with P <= 1/3 (R <= 1/3) are absolutely separable.
    Cited as [15]; the paper's 'absolute separability boundary' restates it.
  • domain assumption Costa-Angelo LS3 identity: three-measurement linear steering violation is equivalent to B_NL > 1.
    Borrowed from Ref [11] without derivation; it is load-bearing for the claim that the C envelope also certifies steering.
  • domain assumption Local time reversal equates to partial transposition in the LU-invariant framework.
    Main text: 'local time reversal equates to partial transposition (PT) in an LU-invariant framework'; this nonstandard identification converts time-odd generators into PT-negativity.
  • ad hoc to paper Irreducible A-sector generator presence guarantees negative eigenvalues under PT.
    Methods, 'The QC envelopes': the headline NPT guarantee rests on this one-sentence assertion, which is the central claim restated as a mechanism.
  • ad hoc to paper The convex hull of V_pure, V_cor, and V_hinge points is the absolute kinematic limit for each m-quantum tier.
    Methods, steps 1-4; argued via 'It is not difficult to see why this algorithm works', with no proof of global optimality.
  • ad hoc to paper Hole-free completeness holds for arbitrary dimensions: no hidden positivity constraints can carve holes in the interior.
    Conclusion: 'fixing the outer boundaries fixes the entire feasible region'; asserted by continuity from the two-qubit parametrization.
  • domain assumption The Q=0 boundary is the outer positivity wall in general dimensions.
    SI: 'the absolute feasibility boundary remains universally anchored by the Q=0 limit'; used to delimit the feasible (X,Y) region beyond two qubits.

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read the original abstract

The diversity of quantum correlations -- discord, entanglement, steering, and Bell nonlocality -- disappears at the kinematic level of observable second moments. By treating state purity as a finite resource, we introduce a local-unitary-invariant budget that splits these moments into local and nonlocal sectors. This maps quantum systems onto compact, two-dimensional manifolds whose topology is governed by purity and time-reversal symmetry. This dimensional reduction reveals a deep structural link: exceeding classical capacity limits requires the activation of intrinsically time-odd generators, providing a dimension-agnostic guarantee of negative partial transpose (NPT) entanglement. For two qubits, this geometry is analytically solvable; a single boundary isolates classical correlations, while nested regions define thresholds for steering and Bell nonlocality, alongside bounds on non-stabiliser magic. Beyond two qubits, dimensional bottlenecks enforce the kinematic limits on correlations. Because this macroscopic representation is completely determined by global and marginal purities, it bypasses the exponential scaling of full-state tomography. Thus, whenever an $n$-partite state's correlations exceed the classical capacity limits, its NPT entanglement is certified by only $n+1$ purity measurements, with sample complexity independent of Hilbert space dimension. By coarse-graining over gauge-like first moments, this geometry acts as a thermodynamic phase diagram, exposing the hierarchy of quantum resources and their dynamic redistribution under decoherence.

Figures

Figures reproduced from arXiv: 2603.03887 by Maaz Khan, Subhadip Mitra.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
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Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6 [PITH_FULL_IMAGE:figures/full_fig_p014_6.png] view at source ↗
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Figure 7. Figure 7: FIG. 7 [PITH_FULL_IMAGE:figures/full_fig_p015_7.png] view at source ↗
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Figure 8. Figure 8: FIG. 8 [PITH_FULL_IMAGE:figures/full_fig_p016_8.png] view at source ↗
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Figure 9. Figure 9: FIG. 9 [PITH_FULL_IMAGE:figures/full_fig_p017_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10 [PITH_FULL_IMAGE:figures/full_fig_p018_10.png] view at source ↗

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Reference graph

Works this paper leans on

30 extracted references · 16 linked inside Pith

  1. [1]

    Introducing Quantum Discord,

    Harold Ollivier and Wojciech H. Zurek, “Introducing Quantum Discord,” Phys. Rev. Lett.88, 017901 (2001), arXiv:quant-ph/0105072

    Pith/arXiv arXiv 2001

  2. [2]

    This maps to a distinct guaranteed- violation ellipse in the budget plane:Y> p 4/5−3X 2/5

    must vi- olate the inequality. This maps to a distinct guaranteed- violation ellipse in the budget plane:Y> p 4/5−3X 2/5. Beyond two qubits For systems larger than2⊗2or2⊗3, positive PT no longer guarantees separability due to bound entangle- ment, though a general notion of biseparability exists for composite systems [14, 15]. However, a negative PT (NPT)...

  3. [3]

    Can quantum mechanical description of physical reality be con- sidered complete?

    Albert Einstein, Boris Podolsky, and Nathan Rosen, “Can quantum mechanical description of physical reality be con- sidered complete?” Phys. Rev.47, 777–780 (1935)

    1935

  4. [4]

    Probability relations between separated systems,

    E. Schrödinger, “Probability relations between separated systems,” Math. Proc. Cambridge Phil. Soc.32, 446–452 11 (2008)

    2008

  5. [5]

    On the Einstein-Podolsky-Rosen paradox,

    J. S. Bell, “On the Einstein-Podolsky-Rosen paradox,” Physics Physique Fizika1, 195–200 (1964)

    1964

  6. [6]

    Stabilizer Rényi Entropy,

    Lorenzo Leone, Salvatore F. E. Oliviero, and Alioscia Hamma, “Stabilizer Rényi Entropy,” Phys. Rev. Lett.128, 050402 (2022), arXiv:2106.12587 [quant-ph]

    Pith/arXiv arXiv 2022

  7. [7]

    Description of States in Quantum Mechanics by Density Matrix and Operator Techniques,

    U. Fano, “Description of States in Quantum Mechanics by Density Matrix and Operator Techniques,” Rev. Mod. Phys. 29, 74–93 (1957)

    1957

  8. [8]

    Separability criterion for density matri- ces,

    Asher Peres, “Separability criterion for density matri- ces,” Phys. Rev. Lett.77, 1413–1415 (1996), arXiv:quant- ph/9604005

    arXiv 1996

  9. [9]

    Separability criterion and inseparable mixedstateswithpositivepartialtransposition,

    Pawel Horodecki, “Separability criterion and inseparable mixedstateswithpositivepartialtransposition,”Phys.Lett. A232, 333 (1997), arXiv:quant-ph/9703004

    Pith/arXiv arXiv 1997

  10. [10]

    Local de- scription of quantum inseparability,

    Anna Sanpera, Rolf Tarrach, and Guifré Vidal, “Local de- scription of quantum inseparability,” Phys. Rev. A58, 826– 830 (1998)

    1998

  11. [11]

    Necessary and Sufficient Condition for Nonzero Quan- tum Discord,

    Borivoje Dakić, Vlatko Vedral, and Časlav Brukner, “Necessary and Sufficient Condition for Nonzero Quan- tum Discord,” Phys. Rev. Lett.105, 190502 (2010), arXiv:1004.0190 [quant-ph]

    Pith/arXiv arXiv 2010

  12. [12]

    Quantification of einstein-podolsky-rosen steering for two-qubit states,

    A. C. S. Costa and R. M. Angelo, “Quantification of einstein-podolsky-rosen steering for two-qubit states,” Phys. Rev. A93, 020103 (2016)

    2016

  13. [13]

    Proposed experiment to test local hidden variable theories,

    John F. Clauser, Michael A. Horne, Abner Shimony, and Richard A. Holt, “Proposed experiment to test local hidden variable theories,” Phys. Rev. Lett.23, 880–884 (1969)

    1969

  14. [14]

    Violat- ing Bell inequality by mixed spin-12states: necessary and sufficient condition,

    R. Horodecki, P. Horodecki, and M. Horodecki, “Violat- ing Bell inequality by mixed spin-12states: necessary and sufficient condition,” Phys. Lett. A200, 340–344 (1995)

    1995

  15. [15]

    On the volume of the set of mixed en- tangled states,

    Karol Zyczkowski, Pawel Horodecki, Anna Sanpera, and Maciej Lewenstein, “On the volume of the set of mixed en- tangled states,” Phys. Rev. A58, 883 (1998), arXiv:quant- ph/9804024

    arXiv 1998

  16. [16]

    Largest separa- ble balls around the maximally mixed bipartite quan- tum state,

    Leonid Gurvits and Howard Barnum, “Largest separa- ble balls around the maximally mixed bipartite quan- tum state,” Phys. Rev. A66, 062311 (2002), arXiv:quant- ph/0204159

    arXiv 2002

  17. [17]

    Magic states of top quarks,

    Chris D. White and Martin J. White, “Magic states of top quarks,” Phys. Rev. D110, 116016 (2024), arXiv:2406.07321 [hep-ph]

    Pith/arXiv arXiv 2024

  18. [18]

    Nielsen and Isaac L

    Michael A. Nielsen and Isaac L. Chuang,Quantum Com- putation and Quantum Information(Cambridge University Press, 2012)

    2012

  19. [19]

    H. P. Breuer and F. Petruccione,The theory of open quan- tum systems(2002)

    2002

  20. [20]

    Protectingentanglementfromcorrelatedam- plitude damping channel using weak measurement and quantum measurement reversal,

    Xing Xiao, Yao Yao, Ying-Mao Xie, Xing-Hua Wang, and Yan-LingLi,“Protectingentanglementfromcorrelatedam- plitude damping channel using weak measurement and quantum measurement reversal,” Quant. Inf. Proc.15, 3881–3891 (2016), arXiv:1602.01998 [quant-ph]

    Pith/arXiv arXiv 2016

  21. [21]

    Three qubits can be en- tangledintwoinequivalentways,

    W. Dur, G. Vidal, and J. I. Cirac, “Three qubits can be en- tangledintwoinequivalentways,”Phys.Rev.A62,062314 (2000), arXiv:quant-ph/0005115

    Pith/arXiv arXiv 2000

  22. [22]

    A measurement schemeforpuritybasedontwotwo-bodygates,

    Hiromichi Nakazato, Toru Tanaka, Kazuya Yuasa, Giuseppe Florio, and Saverio Pascazio, “A measurement schemeforpuritybasedontwotwo-bodygates,”Phys.Rev. A85, 042316 (2012), arXiv:1201.2736 [quant-ph]

    Pith/arXiv arXiv 2012

  23. [23]

    Experimen- tal SWAP test of infinite dimensional quantum states,

    Chi-Huan Nguyen, Ko-Wei Tseng, Gleb Maslennikov, H. C. J. Gan, and Dzmitry Matsukevich, “Experimen- tal SWAP test of infinite dimensional quantum states,” (2021), arXiv:2103.10219 [quant-ph]

    Pith/arXiv arXiv 2021

  24. [24]

    Predictingmanypropertiesofaquantumsystemfromvery few measurements,

    Hsin-Yuan Huang, Richard Kueng, and John Preskill, “Predictingmanypropertiesofaquantumsystemfromvery few measurements,” Nature Phys.16, 1050–1057 (2020), arXiv:2002.08953 [quant-ph]

    Pith/arXiv arXiv 2020

  25. [25]

    Measuring Trρn on Single Copies ofρUsing Random Measurements,

    S. J. van Enk and C. W. J. Beenakker, “Measuring Trρn on Single Copies ofρUsing Random Measurements,” Phys. Rev. Lett.108, 110503 (2012), arXiv:1112.1027 [quant- ph]. 12 Supplementary Information: Kinematic budget of quantum correlations Maaz Khan1 and Subhadip Mitra1,2 1Center for Computational Natural Sciences and Bioinformatics, International Institute...

    Pith/arXiv arXiv 2012

  26. [26]

    Correlation constraints and the Bloch ge- ometry of two qubits,

    Simon Morelli, Christopher Eltschka, Marcus Huber, and Jens Siewert, “Correlation constraints and the Bloch ge- ometry of two qubits,” Phys. Rev. A109, 012423 (2024), arXiv:2303.11400 [quant-ph]

    Pith/arXiv arXiv 2024

  27. [27]

    Protecting three-dimensional entanglement from the correlated amplitude damping channel,

    Xing Xiao, Wen-Rui Huang, Tian-Xiang Lu, and Yan-Ling Li, “Protecting three-dimensional entanglement from the correlated amplitude damping channel,” Chin. J. Phys.97, 223–238 (2025), arXiv:2406.18796 [quant-ph]

    Pith/arXiv arXiv 2025

  28. [28]

    Be- yond Qubits: An Extensive Noise Analysis for Qutrit Quan- tum Teleportation,

    ArunSebastian,Afnan.N.Mansar, andN.C.Randeep,“Be- yond Qubits: An Extensive Noise Analysis for Qutrit Quan- tum Teleportation,” Int. J. Theor. Phys.62, 258 (2023), arXiv:2309.12163 [quant-ph]

    Pith/arXiv arXiv 2023

  29. [29]

    Going Beyond Bell’s Theorem,

    Daniel M. Greenberger, Michael A. Horne, and Anton Zeilinger, “Going Beyond Bell’s Theorem,” Fundam. Theor. Phys.37, 69–72 (1989), arXiv:0712.0921 [quant-ph]

    Pith/arXiv arXiv 1989

  30. [30]

    Virtual DistillationforQuantumErrorMitigation,

    William J. Huggins, Sam McArdle, Thomas E. O’Brien, Joonho Lee, Nicholas C. Rubin, Sergio Boixo, K. Birgitta Whaley, Ryan Babbush, and Jarrod R. McClean, “Virtual DistillationforQuantumErrorMitigation,”Phys.Rev.X11, 041036 (2021), arXiv:2011.07064 [quant-ph]. 18

    Pith/arXiv arXiv 2021