Pith. sign in

REVIEW 2 major objections 5 minor 58 references

Effects of coherent and incoherent measurement imperfections on multipartite quantum nonlocality and quantum key distribution

T0 review · 2 major / 5 minor · reviewed 2026-08-02 · deepseek-v4-flash

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

Pith's one-line read Measurement imperfections degrade multipartite Bell violations by two closed-form laws—S′ = S_Q cos(mθ) and S′ = S_Q(2p−1)^n—and the same degraded values force tighter precision for secret-key generation than for nonlocality certification.

desk verdict Bell-degradation half is solid and useful; the key-rate half has an internal entropy-accounting error that shifts the headline threshold. read the letter →

arxiv 2607.13645 v1 pith:HIVAKOOF submitted 2026-07-15 quant-ph

Qiong Wang , Wen-Long Qiao , Qing Chen , Liu-Jun Wang This is my paper · ORCID
classification quant-ph MSC 81P4081P4581P15
keywords BellinequalitiesGHZstatesmeasurementmisalignmentoutcomeflippingmultipartitenonlocalityquantumkeydistributionSvetlichnyinequalityMABK
topics The Measurement Problem
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 paper sets out to establish that two physically distinct measurement imperfections—coherent angular misalignment and incoherent outcome flipping—degrade n-partite GHZ Bell violations in closed, predictable forms, and that the same degradation, when fed into a Devetak–Winter key-rate bound, makes secret-key generation demand tighter measurement precision than nonlocality certification alone. If correct, experimenters get quantitative tolerances: under common rotation with m faulty parties, Mermin, Svetlichny, and MABK values fall as S_Q cos(mθ), so violation windows repeat periodically and each narrows as 1/n; under outcome flipping, values fall as S_Q(2p−1)^n, with a single threshold p_cr = ((S_C/S_Q)^{1/n}+1)/2 that rises with n for MABK and odd-n Mermin but falls for Svetlichny. The authors connect the degraded Svetlichny value to a convex-combination attack model and derive a universal positive-key condition χ > 2/(4−√2) ≈ 0.77, stricter than the nonlocality threshold χ > 1/√2. A fair reader should take the paper as providing these benchmark laws, with the caveat that the key-rate conclusions rest on the attack model the paper adopts rather than on a general security proof.

What carries the argument

The load-bearing objects are two degradation mechanisms: coherent rotation of each local measurement by angle θ, which accumulates as a phase mθ in the full correlation and produces S′ = S_Q cos(mθ); and stochastic outcome flipping with correct-readout probability p, which multiplies every n-party correlation by (2p−1)^n and produces S′ = S_Q(2p−1)^n. These formulas, together with the classical bound S_C and quantum maximum S_Q of the Mermin, Svetlichny, and MABK inequalities, fix all certification thresholds. For key rates, the additional machinery is a convex-combination attack model in which the observed Bell value splits into a locally explainable part accessible to Eve and a maximally n

What would settle it

Perform a three-party Svetlichny test on a GHZ state while independently rotating the measurement bases by a controlled angle θ and, in a separate run, flipping each recorded outcome with controlled probability 1−p; if the observed Bell value departs from S_Q cos(3θ) or from S_Q(2p−1)^3 faster than these formulas, the degradation laws fail. For the key-rate claim, compute Eve's optimal guessing probability under a collective attack on the same state at the same observed Bell value; if it exceeds (1+q_L)/2 from the convex-combination model, the threshold χ > 2/(4−√2) is not security-relevant.

Watch

Extended reading notes

Core claim

The central claim is that in n-partite GHZ Bell tests with orthogonality-preserving coherent misalignment affecting m parties, every considered Bell value obeys S′ = S_Q cos(mθ), producing periodic violation windows centered at 2kπ/n with half-width arccos(S_C/S_Q)/n that shrinks as 1/n; while under incoherent outcome flipping with correct-readout probability p, every full correlation is multiplied by (2p−1)^n, yielding S′ = S_Q(2p−1)^n and a single threshold p_cr = ((S_C/S_Q)^{1/n}+1)/2. For the Svetlichny inequality, S_C/S_Q = 1/√2, so its windows are half as wide as Mermin/MABK windows and its flipping threshold decreases with n, while MABK and odd-n Mermin become more tolerant of flippin

Load-bearing premise

The key-rate thresholds hold only under the paper's convex-combination attack model—that Eve's information is fully captured by a mixture of a local part she knows completely and a nonlocal part she guesses with probability 1/2—and the paper does not prove this model covers general collective or coherent attacks; a secondary fragile step is the assumption that the key-generation correlation degrades by the same factor cos(nθ) as the Bell value, verified only for n = 3.

Editorial extensions

If this is right

  • For coherent misalignment, Bell violation persists inside repeating angular windows, but each window is only arccos(S_C/S_Q)/n wide; the Svetlichny window is always half as wide as the Mermin/MABK window, asymptotically π/(4n) versus π/(2n).
  • For incoherent outcome flipping, MABK and odd-n Mermin tolerate a finite large-n flip probability approaching (2−√2)/4 ≈ 0.146, while the Svetlichny flip tolerance decays to zero as n grows.
  • Secret-key generation from the Svetlichny value requires χ > 2/(4−√2) ≈ 0.77, so the key window, with half-width arccos[2/(4−√2)]/n ≈ 0.218π/n, sits strictly inside the nonlocality window of half-width π/(4n); there is a parameter region where genuine multipartite nonlocality is certified but no positive key rate is obtained.
  • For Werner states with visibility v, the threshold becomes v > 2/[(4−√2)χ], so larger n demands higher state visibility to tolerate the same measurement imperfection.

Reading between the lines

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

  • A testable extension: on a single 3-GHZ source, measure the Bell value versus θ and versus 1−p; the two curves should cross the classical bound at arccos(1/√2)/3 and (2^{−1/6}+1)/2, giving a direct check of both scaling laws and of their claimed universality across the Mermin, MABK, and Svetlichny inequalities.
  • Because the key-rate condition χ > 2/(4−√2) is derived only inside the convex-combination attack model, the paper's claim that key generation is stricter than nonlocality should be read as a statement about that model; a fully device-independent proof would need to establish the same bound against general collective or coherent attacks, which the paper leaves open.
  • The paper verifies the equality χ1 = χ2 = cos(nθ) only for n = 3; for n > 3 the key-window positions are a plausible extrapolation, and checking them directly with the stabilizer correlations of the n-GHZ state is the natural next step.
  • If the scaling laws hold, they suggest a practical calibration strategy: use the sharp 1/n shrinkage of Svetlichny windows as a sensitive in-situ test of basis alignment, and use the flat (2−√2)/4 large-n limit as a readout-error budget that can be spent before mitigation is needed.
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

2 major / 5 minor

Summary. The paper derives analytic degradation laws for three families of multipartite Bell inequalities (Mermin, Svetlichny, MABK) in n-partite GHZ Bell tests under two models of measurement imperfection: coherent common angular misalignment and incoherent outcome flipping. For coherent misalignment with m faulty parties and θ1=θ2=θ, all three Bell values reduce to S' = S_Q cos(mθ), giving periodic violation windows centered at 2πk/n with widths O(1/n); explicit critical angles are given in Eqs. (14)–(16). For incoherent flipping, all n-partite correlations are attenuated by (2p−1)^n, yielding the single threshold p_cr = ((S_C/S_Q)^{1/n}+1)/2 (Eq. (23)); the MABK threshold approaches (2−√2)/4 for large n, while the Svetlichny threshold decreases to zero. The paper then connects the degraded Svetlichny value to asymptotic Devetak–Winter key rates via a convex-combination attack model (Eqs. (27)–(32)), concluding that positive key generation requires stricter measurement tolerances than genuine multipartite nonlocality certification, with thresholds in Eqs. (33), (34), and Werner visibility thresholds in Eq. (39).

Significance. The Bell-degradation part is a clean, parameter-free contribution: the cos(mθ) and (2p−1)^n laws are derived analytically, reduce correctly in the α=0 case, and directly provide quantitative tolerance benchmarks for multipartite Bell certification. The different scaling with n for MABK versus Svetlichny is a useful and falsifiable prediction. The key-rate part is not yet at the same standard: it depends on an imported, unproven attack model and, as discussed below, contains an entropy-accounting error. With those corrected, the comparison between nonlocality certification and key generation could be a valuable result.

major comments (2)
  1. [Section 4, Eq. (30a)] The conditional entropy H(A1|E) does not follow from the stated attack model. The model says Eve has full information on the local component (probability q_L) and a random guess (success 1/2) on the nonlocal component. For that c-q state, H(A1|E) = q_L·0 + (1−q_L)·1 = 1−q_L. The expression h((1+q_L)/2) is the entropy of a binary variable whose optimal guessing probability is (1+q_L)/2; it is an upper bound, not the actual entropy of the described state. Since Eq. (32) is claimed as a lower bound on r_DW, using h((1+q_L)/2) overestimates H(A1|E) and therefore the key rate. Solving 1−q_L = h((1−χ)/2) with q_L = (2−2χ)/(2−√2) gives χ ≈ 0.829 instead of 2/(4−√2) ≈ 0.773; Eqs. (33), (34), (39) and Fig. 5 all shift. The qualitative conclusion that key generation is stricter may survive, but the quantitative benchmark is not supported by the text as written.
  2. [Section 4, Eqs. (27)–(32) and final paragraph] The convex-combination decomposition S' = q_L S_C + q_NL S_Q and the claim that Eve's optimal guessing probability on the nonlocal fraction is exactly 1/2 are imported from Refs. [48,49] and are not proven to be optimal against general collective or coherent attacks. The final paragraph concedes that more general eavesdropping strategies are future work, but the abstract and conclusion present the key-rate constraints without this caveat. Please either restrict all key-rate claims explicitly to this model, or provide an argument that the convex-combination attack gives a valid lower bound against a well-defined adversarial class. As written, the 'Devetak–Winter bound' terminology overstates the security scope.
minor comments (5)
  1. [Section 4.1 / Table 2] The equality χ1 = χ2 = cos(nθ) is verified only for n=3 in Table 2. For general n, a one-line proof using the fact that any valid GHZ key stabilizer contains an odd number of σy, hence |sin(rπ/2+nθ)| = cos(nθ), would make the statement self-contained.
  2. [Eq. (30a) attribution] Please verify Eq. (30a) against Refs. [48,49] and cite the exact derivation. If those references use a different attack model in which h((1+q_L)/2) is exact, the text should say so explicitly; if not, the formula should be corrected per the major comment.
  3. [Eqs. (18a)–(18b)] The notation ∑_{x_i} and ∑_{\{x_i\}} is used inconsistently; define the parity condition ∑_i x_i ≡ 0 (mod 2) clearly before first use.
  4. [Figure 2 caption] The caption refers to 'dark and light dashed lines' marking analytical lower and upper critical angles, but the figure rendering does not clearly distinguish them. Please ensure the printed figure is legible and the legend matches the caption.
  5. [References [45,46]] A few references carry 2026 volume/page numbers. If these are preprints or accepted papers, please add arXiv identifiers or publication status to aid verification.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the Bell degradation laws, violation windows, and threshold conditions are parameter-free analytic consequences of the stated misalignment and flipping models.

full rationale

The derivation chain is self-contained where it is predictive. The coherent-misalignment results (Eqs. (9)-(16)) are obtained by substituting the rotated observables into the Mermin/Svetlichny/MABK operators and evaluating on the GHZ state; no fitted parameter or target quantity is fed back into the calculation. The incoherent-flipping scaling S'_Q = S_Q(2p-1)^n (Eq. (22)) follows from the readout-channel transformation (Eq. (20)), and the thresholds (Eqs. (23)-(26)) are simply the solutions of S'=S_C. The key-rate analysis (Sec. 4) does import an external convex-combination attack model and the entropy expression H(A1|E)=h((1+q_L)/2) from Refs. [48,49], which are by different authors; this makes the key-rate benchmark model-dependent rather than circular. The paper itself concedes the limitation in the final paragraph ('more general eavesdropping strategies beyond the convex-combination attack model'). A possible correctness concern is that the stated attack description ('full information about the local component') would suggest H(A1|E)=1-q_L rather than the quoted h((1+q_L)/2); but that is an internal-model/security-analysis issue, not a circularity, since the threshold is an algebraic consequence of the stated expression rather than identical to the input. No self-citation chain, uniqueness import, or fit-then-predict structure appears. Score 0.

Assumptions & free parameters 0 free parameters · 5 assumptions · 0 invented entities

The central claims rest on three model choices (unitary misalignment rotation, setting-independent outcome flipping, convex-combination eavesdropping) plus the standard Bell/GHZ apparatus. No free parameters are fitted to data — θ and p are swept inputs, and all thresholds are solved rather than fit. No invented entities. The convex-combination model is the heaviest assumption: it is imported from Refs. [48,49] and carries the entire key-rate half of the paper.

assumptions (5)
  • standard math Standard n-qubit Bell/GHZ framework: the GHZ state (Eq. 1), dichotomic x–y-plane observables, and the Mermin/Svetlichny/MABK inequalities with their classical bounds (Table 1).
    Textbook background assumed throughout; the operators and bounds are standard, cited to Refs. [11–15].
  • domain assumption Coherent misalignment is a unitary rotation of each local observable, Ã = cosθ A + sinθ A⊥ (Eq. 7), and all threshold results restrict to the orthogonality-preserving common rotation θ1 = θ2.
    Physically motivated but a modeling choice; the general-α formulas (Eqs. 11–13) show non-orthogonal misalignment changes the violation landscape, so the headline thresholds cover only the common-rotation branch.
  • domain assumption Outcome flipping is a setting-independent classical channel with equal correct-readout probability p for both outcomes at every party (Eq. 8), and the probabilistic derivation applies only to symmetric full-correlation inequalities (Appendix B: CHSH, Svetlichny, Mermin, MABK qualify).
    The (2p−1)^n scaling follows from independence and symmetry of the flip noise; correlated or setting-dependent readout errors would destroy the single-threshold structure.
  • ad hoc to paper Convex-combination attack model: S′ = q_L S_C + q_NL S_Q with Eve's guessing probability exactly 1/2 on the nonlocal fraction, and Devetak–Winter rate r ≥ H(A1|E) − H(A1|A2...An) (Eqs. 27–32).
    Imported from Refs. [48,49]; this model is the entire basis of the key-rate claims and is not validated against general attacks — the paper's own final paragraph concedes this.
  • domain assumption Under common rotation the key-generation stabilizer degrades by the same factor as the Bell value, χ1 = χ2 = cos(nθ) (or (2p−1)^n) (Sec. 4.1).
    Directly verified for the four n=3 valid settings in Table 2; asserted for general n. If a chosen stabilizer degraded differently, the QBER term and hence the key-rate threshold would change.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Effects of coherent and incoherent measurement imperfections on multipartite quantum nonlocality and quantum key distribution." pith.science (2026). https://pith.science/paper/HIVAKOOF

@misc{pith2026260713645,
  author       = {Pith},
  title        = {Pith review of: Effects of coherent and incoherent measurement imperfections on multipartite quantum nonlocality and quantum key distribution},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/HIVAKOOF}},
  note         = {Machine review of arXiv:2607.13645}
}
abstract

Multipartite Bell nonlocality is a central resource for device-independent quantum information protocols, but its practical certification is inevitably affected by imperfect measurements. We analyze how coherent angular misalignment and incoherent outcome flipping affect Bell-value degradation and nonlocality thresholds in $n$-partite GHZ states based on the Mermin, Svetlichny, and Mermin--Ardehali--Belinskii--Klyshko (MABK) inequalities. Coherent misalignment produces periodic angular violation windows whose individual widths shrink with the number of parties. In contrast, incoherent outcome flipping yields a single critical outcome-flipping probability, which increases with $n$ for MABK and the odd-$n$ Mermin inequalities, but decreases with $n$ for the Svetlichny inequality. Connecting the degraded Bell values to asymptotic Devetak--Winter key-rate bounds under a convex-combination attack model shows that secret-key generation imposes stricter constraints on measurement imperfections than nonlocality certification. These results provide quantitative benchmarks for robust multipartite nonlocality certification and key-rate estimation under measurement imperfections.

Figures

Figures reproduced from arXiv: 2607.13645 by the authors.

Figure 1
Figure 1. Evolution of the normalized Mermin violation [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Full angular-domain violation regions under [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. Normalized Bell violation S ′/SC versus the outcome-flipping probability 1 − p for n = 3 and n = 4 GHZ states. Dashed and solid curves correspond to n = 3 and n = 4, respectively. The horizontal dot￾ted line indicates the classical threshold S ′/SC = 1. The monotonic decay of all curves follows from the uni￾form correlation scaling factor (2p − 1)n. For n = 3, the MABK and Mermin curves overlap because the two inequ… view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: Critical outcome-flipping probability 1 − pcr required to violate different multipartite Bell inequalities as a function of the particle number n. The Mermin threshold (green squares) exhibits characteristic parity￾dependent oscillations, reflecting its suboptimality f…
Figure 5
Figure 5. Figure 5: Threshold visibility vth required for positive secret key generation in n-partite Werner states under imperfect measurements. The region above each curve corresponds to v > vth. (a) v p th as a function of the outcome-flipping probability 1−p. (b) v θ th as a function …

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

58 extracted references

  1. [1]

    On the Einstein Podolsky Rosen paradox

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

    1964

  2. [2]

    On the problem of hidden variables in quantum mechanics

    JOHN S. BELL. “On the problem of hidden variables in quantum mechanics”. Rev. Mod. Phys.38, 447–452 (1966)

    1966

  3. [3]

    Bell nonlocality

    Nicolas Brunner, Daniel Cavalcanti, Ste- fano Pironio, Valerio Scarani, and Stephanie Wehner. “Bell nonlocality”. Rev. Mod. Phys. 86, 419–478 (2014)

    2014

  4. [4]

    Advances in quantum cryptography

    S. Pirandola, U. L. Andersen, L. Banchi, M. Berta, D. Bunandar, R. Colbeck, D. En- glund, T. Gehring, C. Lupo, C. Ottaviani, et al. “Advances in quantum cryptography”. Adv. Opt. Photonics12, 1012–1236 (2020)

    2020

  5. [5]

    Fully device-independent quantum key distribu- tion

    Umesh Vazirani and Thomas Vidick. “Fully device-independent quantum key distribu- tion”. Phys. Rev. Lett.113, 140501 (2014). 15

    2014

  6. [6]

    Device-independent quantum key distribution with random postselection

    Feihu Xu, Yu-Zhe Zhang, Qiang Zhang, and Jian-Wei Pan. “Device-independent quantum key distribution with random postselection”. Phys. Rev. Lett.128, 110506 (2022)

    2022

  7. [7]

    Device-independent quan- tum secret sharing with advanced random key generation basis

    Qi Zhang, Jia-Wei Ying, Zhong-Jian Wang, Wei Zhong, Ming-Ming Du, Shu-Ting Shen, Xi-Yun Li, An-Lei Zhang, Shi-Pu Gu, Xing- Fu Wang, et al. “Device-independent quan- tum secret sharing with advanced random key generation basis”. Phys. Rev. A111, 012603 (2025)

    2025

  8. [8]

    Device- independent secret sharing and a stronger form of Bell nonlocality

    M. G. M. Moreno, Samuraí Brito, Ranieri V. Nery, and Rafael Chaves. “Device- independent secret sharing and a stronger form of Bell nonlocality”. Phys. Rev. A101, 052339 (2020)

    2020

Show all 58 references
  1. [9]

    Device-independent quantum secret sharing in arbitrary even dimensions

    Sarbani Roy and Sourav Mukhopadhyay. “Device-independent quantum secret sharing in arbitrary even dimensions”. Phys. Rev. A 100, 012319 (2019)

    2019

  2. [10]

    Random numbers certi- fied by Bell’s theorem

    S. Pironio, A. Acín, S. Massar, A. Boyer de la Giroday, D. N. Matsukevich, P. Maunz, S. Olmschenk, D. Hayes, L. Luo, T. A. Manning, et al. “Random numbers certi- fied by Bell’s theorem”. Nature464, 1021– 1024 (2010)

    2010

  3. [11]

    Extremequantumentan- glement in a superposition of macroscopically distinct states

    N.DavidMermin. “Extremequantumentan- glement in a superposition of macroscopically distinct states”. Phys. Rev. Lett.65, 1838– 1840 (1990)

    1990

  4. [12]

    Distinguishing three- body from two-body nonseparability by a Bell-type inequality

    George Svetlichny. “Distinguishing three- body from two-body nonseparability by a Bell-type inequality”. Phys. Rev. D35, 3066– 3069 (1987)

    1987

  5. [13]

    Bell inequalities with a mag- nitude of violation that grows exponentially with the number of particles

    M. Ardehali. “Bell inequalities with a mag- nitude of violation that grows exponentially with the number of particles”. Phys. Rev. A 46, 5375–5378 (1992)

    1992

  6. [14]

    Interfer- ence of light and bell’s theorem

    A. V. Belinskii and D. N. Klyshko. “Interfer- ence of light and bell’s theorem”. Phys. Usp. 36, 653–693 (1993)

    1993

  7. [15]

    Bell-type inequalities for partial separabil- ity inn-particle systems and quantum me- chanical violations

    Michael Seevinck and George Svetlichny. “Bell-type inequalities for partial separabil- ity inn-particle systems and quantum me- chanical violations”. Phys. Rev. Lett.89, 060401 (2002)

    2002

  8. [16]

    Bell-type inequalities to detect true n-body nonseparability

    Daniel Collins, Nicolas Gisin, Sandu Popescu, David Roberts, and Valerio Scarani. “Bell-type inequalities to detect true n-body nonseparability”. Phys. Rev. Lett. 88, 170405 (2002)

    2002

  9. [17]

    Going beyond Bell’s theorem

    Daniel M. Greenberger, Michael A. Horne, and Anton Zeilinger. “Going beyond Bell’s theorem”. In Menas Kafatos, editor, Bell’s Theorem, Quantum Theory and Conceptions of the Universe. Pages 69–72. Springer, Dor- drecht (1989)

    1989

  10. [18]

    Bell’s theorem without inequalities

    Daniel M. Greenberger, Michael A. Horne, Abner Shimony, and Anton Zeilinger. “Bell’s theorem without inequalities”. Am. J. Phys. 58, 1131–1143 (1990)

    1990

  11. [19]

    Experimentaltestofquantumnon- locality in three-photon Greenberger–Horne– Zeilinger entanglement

    Jian-Wei Pan, Dik Bouwmeester, Matthew Daniell, Harald Weinfurter, and Anton Zeilinger. “Experimentaltestofquantumnon- locality in three-photon Greenberger–Horne– Zeilinger entanglement”. Nature403, 515– 519 (2000)

    2000

  12. [20]

    Efficient quantum key distribution secure against no-signalling eavesdroppers

    Antonio Acín, Serge Massar, and Stefano Pironio. “Efficient quantum key distribution secure against no-signalling eavesdroppers”. New J. Phys.8, 126 (2006)

    2006

  13. [21]

    From Bell’s theorem to secure quantum key distribution

    Antonio Acín, Nicolas Gisin, and Lluis Masanes. “From Bell’s theorem to secure quantum key distribution”. Phys. Rev. Lett. 97, 120405 (2006)

    2006

  14. [22]

    Device-independent security of quantum cryptography against collective at- tacks

    Antonio Acín, Nicolas Brunner, Nicolas Gisin, Serge Massar, Stefano Pironio, and Va- lerio Scarani. “Device-independent security of quantum cryptography against collective at- tacks”. Phys. Rev. Lett.98, 230501 (2007)

    2007

  15. [23]

    Bell nonlocality is not sufficient for the security of standard device-independent quantum key distribution protocols

    Máté Farkas, Maria Balanzó-Juandó, Karol Łukanowski, Jan Kołodyński, and Antonio Acín. “Bell nonlocality is not sufficient for the security of standard device-independent quantum key distribution protocols”. Phys. Rev. Lett.127, 050503 (2021)

    2021

  16. [24]

    Entropy bounds for multiparty device- independent cryptography

    Federico Grasselli, Gláucia Murta, Her- mann Kampermann, and Dagmar Bruß. “Entropy bounds for multiparty device- independent cryptography”. PRX Quantum 2, 010308 (2021)

    2021

  17. [25]

    Quantum states with Einstein–Podolsky–Rosen correlations admit- ting a hidden-variable model

    Reinhard F. Werner. “Quantum states with Einstein–Podolsky–Rosen correlations admit- ting a hidden-variable model”. Phys. Rev. A 40, 4277–4281 (1989)

    1989

  18. [26]

    Exper- imental quantum key distribution with source flaws

    Feihu Xu, Kejin Wei, Shihan Sajeed, Sarah Kaiser, Shihai Sun, Zhiyuan Tang, Li Qian, Vadim Makarov, and Hoi-Kwong Lo. “Exper- imental quantum key distribution with source flaws”. Phys. Rev. A92, 032305 (2015)

    2015

  19. [27]

    Experimen- 16 tal measurement-device-independent quan- tum key distribution with imperfect sources

    Zhiyuan Tang, Kejin Wei, Olinka Bedroya, Li Qian, and Hoi-Kwong Lo. “Experimen- 16 tal measurement-device-independent quan- tum key distribution with imperfect sources”. Phys. Rev. A93, 042308 (2016)

    2016

  20. [28]

    Side-channel-secure quantum key distribution with imperfect vacuum sources

    Cong Jiang, Zong-Wen Yu, Xiao-Long Hu, and Xiang-Bin Wang. “Side-channel-secure quantum key distribution with imperfect vacuum sources”. Phys. Rev. Appl.19, 064003 (2023)

    2023

  21. [29]

    Loss- tolerant quantum cryptography with imper- fect sources

    Kiyoshi Tamaki, Marcos Curty, Go Kato, Hoi-Kwong Lo, and Koji Azuma. “Loss- tolerant quantum cryptography with imper- fect sources”. Phys. Rev. A90, 052314 (2014)

    2014

  22. [30]

    Background level and counter efficiencies required for a loophole-free Einstein–Podolsky–Rosen ex- periment

    Philippe H. Eberhard. “Background level and counter efficiencies required for a loophole-free Einstein–Podolsky–Rosen ex- periment”. Phys. Rev. A47, R747– R750 (1993)

    1993

  23. [31]

    Detection-loophole-free test of quantumnonlocality, andapplications

    B. G. Christensen, K. T. McCusker, J. B. Altepeter, B. Calkins, T. Gerrits, A. E. Lita, A. Miller, L. K. Shalm, Y. Zhang, S. W. Nam, et al. “Detection-loophole-free test of quantumnonlocality, andapplications”. Phys. Rev. Lett.111, 130406 (2013)

    2013

  24. [32]

    Secure quan- tum key distribution with realistic devices

    Feihu Xu, Xiongfeng Ma, Qiang Zhang, Hoi- Kwong Lo, and Jian-Wei Pan. “Secure quan- tum key distribution with realistic devices”. Rev. Mod. Phys.92, 025002 (2020)

    2020

  25. [33]

    Significant- loophole-free test of Bell’s theorem with en- tangled photons

    Marissa Giustina, Marijn A. M. Versteegh, Sören Wengerowsky, Johannes Handsteiner, Armin Hochrainer, Kevin Phelan, Fabian Steinlechner, Johannes Kofler, Jan-Åke Lars- son, Carlos Abellán, et al. “Significant- loophole-free test of Bell’s theorem with en- tangled photons”. Phys...

    2015

  26. [34]

    Loophole-free Bell inequality vi- olation using electron spins separated by 1.3 kilometres

    B. Hensen, H. Bernien, A. E. Dréau, A. Reis- erer, N. Kalb, M. S. Blok, J. Ruitenberg, R. F. L. Vermeulen, R. N. Schouten, C. Abel- lán, et al. “Loophole-free Bell inequality vi- olation using electron spins separated by 1.3 kilometres”. Nature526, 682–686 (2015)

    2015

  27. [35]

    Tomography of quantum detec- tors

    J. S. Lundeen, A. Feito, H. Coldenstrodt- Ronge, K. L. Pregnell, Ch. Silberhorn, T. C. Ralph, J. Eisert, M. B. Plenio, and I. A. Walmsley. “Tomography of quantum detec- tors”. Nat. Phys.5, 27 (2009)

    2009

  28. [36]

    Mitigation of readout noise in near-term quantum devices by classi- cal post-processing based on detector tomog- raphy

    Filip B. Maciejewski, Zoltán Zimborás, and Michał Oszmaniec. “Mitigation of readout noise in near-term quantum devices by classi- cal post-processing based on detector tomog- raphy”. Quantum4, 257 (2020)

    2020

  29. [37]

    Mitigating measurement errors in multiqubit experiments

    Sergey Bravyi, Sarah Sheldon, Abhinav Kandala, David C. Mckay, and Jay M. Gam- betta. “Mitigating measurement errors in multiqubit experiments”. Phys. Rev. A103, 042605 (2021)

    2021

  30. [38]

    Scalable mitigation of measurement errors on quantum computers

    Paul D. Nation, Hwajung Kang, Neereja Sundaresan, and Jay M. Gambetta. “Scalable mitigation of measurement errors on quantum computers”. PRX Quantum2, 040326 (2021)

    2021

  31. [39]

    Detecting crosstalk errors in quantum information processors

    Mohan Sarovar, Timothy Proctor, Kenneth Rudinger, Kevin Young, Erik Nielsen, and Robin Blume-Kohout. “Detecting crosstalk errors in quantum information processors”. Quantum4, 321 (2020)

    2020

  32. [40]

    Imperfect measure- ment settings: Implications for quantum state tomography and entanglement witnesses

    Denis Rosset, Raphael Ferretti-Schöbitz, Jean-Daniel Bancal, Nicolas Gisin, and Yeong-Cherng Liang. “Imperfect measure- ment settings: Implications for quantum state tomography and entanglement witnesses”. Phys. Rev. A86, 062325 (2012)

    2012

  33. [41]

    Genuine multipartite entanglement detection with imperfect measurements: Con- cept and experiment

    Huan Cao, Simon Morelli, Lee A. Rozema, Chao Zhang, Armin Tavakoli, and Philip Walther. “Genuine multipartite entanglement detection with imperfect measurements: Con- cept and experiment”. Phys. Rev. Lett.133, 150201 (2024)

    2024

  34. [42]

    Experimental full-domain mapping of quantum correlation in Clauser–Horne– Shimony–Holt scenarios

    Xin Tong, Zhe He, Yide Zhang, Samuel Solomon, Li Lin, Qiyuan Song, and Lihong V. Wang. “Experimental full-domain mapping of quantum correlation in Clauser–Horne– Shimony–Holt scenarios”. Phys. Rev. Appl. 19, 034049 (2023)

    2023

  35. [43]

    Genuine Einstein–Podolsky–Rosen steering of three-qubit states by multiple sequential observers

    Shashank Gupta, Ananda G. Maity, De- barshi Das, Arup Roy, and A. S. Majumdar. “Genuine Einstein–Podolsky–Rosen steering of three-qubit states by multiple sequential observers”. Phys. Rev. A103, 022421 (2021)

    2021

  36. [44]

    Imprecision plateaus in quantum steering

    Elna Svegborn, Nicola d’Alessandro, Otfried Gühne, and Armin Tavakoli. “Imprecision plateaus in quantum steering”. Phys. Rev. A 111, L020404 (2025)

    2025

  37. [45]

    Reliable quantum steering detection under imperfect measurement

    Ting Zhang, Wenhao Zhang, Jing-Tao Qiu, Leilei Huang, Xiao Yuan, and Qi-Ming Ding. “Reliable quantum steering detection under imperfect measurement”. Phys. Rev. Lett. 136, 090201 (2026)

    2026

  38. [46]

    Imprecise quantum steering inequalities in tripartite systems

    Yan Zhao, Li-Juan Li, Zheng-Peng Xu, Liu Ye, and Dong Wang. “Imprecise quantum steering inequalities in tripartite systems”. Phys. Rev. A113, 042417 (2026)

    2026

  39. [47]

    Quantum metrology with imperfect measurements

    Yink Loong Len, Tuvia Gefen, Alex Retzker, 17 and Jan Kołodyński. “Quantum metrology with imperfect measurements”. Nat. Com- mun.13, 6971 (2022)

    2022

  40. [48]

    Multipartitequantumcryptog- raphy based on the violation of Svetlichny’s inequality

    YangXiang. “Multipartitequantumcryptog- raphy based on the violation of Svetlichny’s inequality”. Eur. Phys. J. D77, 31 (2023)

    2023

  41. [49]

    Impact of imperfect measure- ments on multi-party quantum key distribu- tion

    Yang Xiang. “Impact of imperfect measure- ments on multi-party quantum key distribu- tion”. Results Phys.54, 107051 (2023)

    2023

  42. [50]

    Quantum entanglement

    Ryszard Horodecki, Paweł Horodecki, Michał Horodecki, and Karol Horodecki. “Quantum entanglement”. Rev. Mod. Phys. 81, 865–942 (2009)

    2009

  43. [51]

    Entangle- mentdetection

    Otfried Gühne and Géza Tóth. “Entangle- mentdetection”. Phys.Rep.474, 1–75(2009)

    2009

  44. [52]

    Quadratic Bell inequalities as tests for multipartite entanglement

    Jos Uffink. “Quadratic Bell inequalities as tests for multipartite entanglement”. Phys. Rev. Lett.88, 230406 (2002)

    2002

  45. [53]

    Distil- lation of secret key and entanglement from quantum states

    Igor Devetak and Andreas Winter. “Distil- lation of secret key and entanglement from quantum states”. Proc. R. Soc. A461, 207–235 (2005)

    2005

  46. [54]

    Long- distance device-independent conference key agreement

    Makoto Ishihara, Anders J. E. Bjerrum, Wojciech Roga, Jonatan B. Brask, Ulrik L. Andersen, and Masahiro Takeoka. “Long- distance device-independent conference key agreement”. Phys.Rev.A112, 032429(2025)

    2025

  47. [55]

    Device-independent quantum key activation

    Bora Ulu, Nicolas Brunner, and Mirjam Weilenmann. “Device-independent quantum key activation”. Phys. Rev. Lett.135, 190801 (2025)

    2025

  48. [56]

    Reference- frame-independent quantum key distribu- tion

    Anthony Laing, Valerio Scarani, John G. Rarity, and Jeremy L. O’Brien. “Reference- frame-independent quantum key distribu- tion”. Phys. Rev. A82, 012304 (2010)

    2010

  49. [57]

    Multi-partite entanglement can speed up quantum key distribution in networks

    Michael Epping, Hermann Kampermann, Chiara Macchiavello, and Dagmar Bruß. “Multi-partite entanglement can speed up quantum key distribution in networks”. New J. Phys.19, 093012 (2017)

    2017

  50. [58]

    Typical Werner states sat- isfying all linear Bell inequalities with di- chotomic measurements

    Ming-Xing Luo. “Typical Werner states sat- isfying all linear Bell inequalities with di- chotomic measurements”. Phys. Rev. A97, 042301 (2018). A Different parties experience distinct measurement-direction misalignment Here, we consider party-dependent coherent misalignment, w...

    2018

Pith tools

Reviewed August 2, 2026 · model on record in the stance chip above.