Pith. sign in

REVIEW 3 major objections 4 minor 1 cited by

Security proof for parallel DIQKD

T0 review · 3 major / 4 minor · reviewed 2026-08-06 · deepseek-v4-flash

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

Pith's one-line read Parallel DIQKD based on the CHSH game is proven secure, with a positive asymptotic key rate.

desk verdict Fresh and honest proof strategy for CHSH-based parallel DIQKD, but the one-shot security rests on unproven companion results and a sketched adaptation; worth serious review, not yet self-contained. read the letter →

arxiv 2507.03991 v1 pith:WJC5ZV2D submitted 2025-07-05 quant-ph cs.ITmath.IT

Ashutosh Marwah , Frédéric Dupuis This is my paper · ORCID
classification quant-phcs.ITmath.IT
keywords device-independentquantumkeydistributionparallelDIQKDCHSHgameanchorednon-localgamesrepetitionentropyaccumulationsmoothmin-entropycryptography
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 claims a security proof for a device-independent quantum key distribution protocol in which Alice and Bob play $n$ CHSH-based games in parallel, with no sequential ordering of rounds. The proof establishes that Alice's raw key has smooth min-entropy linear in $n$ against an eavesdropper whenever the test-round winning probability is above threshold. The central move is to show that the answers on a random small subset of games can be approximated by a single-round strategy for the anchored $3\mathrm{CHSH}^\perp$ game, so that per-round randomness bounds apply. Those bounds are assembled by an entropy accumulation theorem for unstructured (parallel) processes, yielding a positive asymptotic key rate for suitable parameters. If correct, this is the first parallel DIQKD security proof based on CHSH rather than on the Magic Square game.

What carries the argument

The load-bearing objects are the $\alpha$-anchored $3\mathrm{CHSH}$ game ($3\mathrm{CHSH}^\perp$), the dependency-breaking variable $R_{-i}=(\Omega_{[n]\setminus(C\cup\{i\})}, X_C,Y_C,A_C,B_C)$, and the unitaries $U^{E_A}_{r_{-i},x}$, $V^{E_B}_{r_{-i},y}$ from anchored parallel repetition that move the state prepared under anchor questions close to the state at index $i$ with real questions. These turn the parallel state into the channel $M_j$ of Box 2, whose output includes the question, test bit, and answer for one raw-key position. The testing map records $W_j=V(X_j,Y_j,A_j,B_j)$ when $T_j=1$ and $\perp$ otherwise, and the piecewise-linear function $\bar{F}_{\alpha,\nu}$ built from Lemma 2.3 is a min-tradeoff function for these channels. Theorem 7.2, the unstructured approximate entropy accumulation theorem, is what converts the closeness of the real partial states to the simulated channel outputs into a linear smooth min-entropy bound; the approximations enter through the parameters $\epsilon$, $\mu$, and $\mu'$ in the bound.

What would settle it

One concrete check is to take a two-round or three-round instance of Protocol 1 with an explicit honest strategy and compute the trace norm in Eq. 92 between the real partial state and the Box 2 simulation, verifying the claimed $O(\delta^{1/16}/\alpha^3)$ bound; a violation would break the chain at its first step. A more direct falsifier would be a counterexample to Theorem 7.2, namely a state and channels satisfying the approximation condition of Eq. 82 for which the smooth min-entropy bound of Eq. 83 does not hold.

Watch

Extended reading notes

Core claim

The paper's central claim is that Protocol 1, built from the $n$-fold $3\mathrm{CHSH}^\perp$ game with a testing subset of size $t=\delta n/(\log|A||B|+\delta)$, generates a secret key with positive asymptotic rate. The proof decomposes the large parallel device into single-round devices: for a fixed subset $C$ of earlier raw-key indices, Proposition 5.1 supplies unitaries that map a shared state prepared with anchor questions to a state close to the real one at a random index outside $C$, and the resulting strategy simulates the real answers while winning the $3\mathrm{CHSH}^\perp$ game with roughly the same probability. Lemma 2.3 then gives a conditional-entropy lower bound for a single $3\mathrm{CHSH}^\perp$ round, and this is converted into an affine min-tradeoff function for each of the $t$ raw-key positions. The unstructured approximate entropy accumulation theorem (Theorem 7.2, proven in the companion paper) turns the per-position approximation into the smooth min-entropy bound of Eq. 112, and chain-rule arguments remove Bob's answers, add testing leakage, and subtract the reconciliation cost to obtain Eq. 118, an $\Omega(n)$ lower bound for the final key length.

Load-bearing premise

The load-bearing premise is that the unstructured approximate entropy accumulation theorem stated as Theorem 7.2, proven only in the companion paper, is correct and can be applied to the approximate single-round channels constructed here; if that theorem fails, or does not cover this approximation structure, the security proof collapses.

Editorial extensions

If this is right

  • For suitable choices of $\alpha$, $\nu$, $\delta$, $\gamma$, and $\omega_{\mathrm{th}}$, Protocol 1 has a positive asymptotic key rate; Eq. 118 lower-bounds the key length by $\Theta(n)$ after accounting for information reconciliation.
  • Smooth min-entropy accumulates linearly in $t$ even though the answers are produced by a single parallel measurement rather than a sequential process; this is the property supplied by the unstructured approximate entropy accumulation theorem.
  • The protocol tolerates noise: $\omega_{\mathrm{th}}$ can be chosen around $0.84$, below the maximal quantum winning probability, so experimental imperfections do not break the proof.
  • The proof couples rate to security: for a security parameter of size $O(\epsilon_s)$, the rate is only $\Omega(\epsilon_s^{192})$, making the protocol a proof of concept rather than a practical scheme.
  • The anchored-simulation route may apply to other non-local games as well, not only CHSH; the paper offers this as a general technique.

Reading between the lines

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

  • Editorial inference: if the unstructured approximate entropy accumulation theorem can be sharpened so the smoothing parameter no longer depends on the approximation parameter, the rate-security coupling $\Omega(\epsilon_s^{192})$ would likely improve; the paper identifies this strengthening as future work.
  • Editorial inference: the same single-round simulation chain suggests a template for parallel device-independent randomness expansion, except that the test questions must remain hidden; the paper explicitly notes this leakage as the obstacle.
  • Editorial inference: the approach should transfer to any anchored game with a single-round entropy bound analogous to Lemma 2.3; checking this on small non-CHSH games would show how general the technique really is.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 4 minor

Summary. The manuscript presents a security proof for a parallel device-independent QKD protocol based on the CHSH game. The protocol (Protocol 1) lets Alice and Bob play n copies of the anchored 3CHSH⊥ game in parallel, using a shared seed Ω; after a random subset J of size t is selected, a random sub-subset S is tested, and Alice's answers on J are used as the raw key. The central technical idea is to import techniques from anchored parallel repetition [BVY21]: for each index in J, the relevant partial state is approximated by the output of a single-round 3CHSH⊥ strategy (Lemmas 6.2–6.5 and Claim 7.3), so that the single-round entropy bound of Lemma 2.3 applies. Section 6 gives a von Neumann-entropy version of this argument with linear rate t·(F(gα,ν(ωth)) − O(ε/ν + δ^{1/16}/(α^3ν) log(1/δ)) − h(2α+ν+Q)). Section 7 converts this into a one-shot smooth min-entropy bound using the 'unstructured approximate entropy accumulation theorem' stated as Theorem 7.2 and imported from the authors' companion paper [MD24b]. The resulting key-rate bound is Eq. (118): H^{μ'+8ε'}_min(AJ | J T^t_1 Ω^n_1 E X_S A_S) − leak_IR ≥ t((1−α)F(g_{α,ν}(ωth)) − O(√μ/(νγ)) − 2h(2(ν+α+δ1)) − 2 log|A| γ) − O(1), which is Ω(n) for suitable parameter choices. The paper is candid that the security parameter and key rate are coupled (roughly Õ(ε_s) security for rate Ω(ε_s^{192})).

Significance. If the central claims are correct, this would be the first security proof for a parallel DIQKD protocol based on the CHSH game, and it would introduce a proof paradigm that combines anchored parallel repetition with a non-sequential approximate entropy accumulation theorem. Compared with previous parallel DIQKD proofs based on the Magic Square game [JMS20, Vid17], the protocol does not require uniform product question distributions, and the approach is potentially more general, as the anchoring construction can be applied to other games. The manuscript also has genuine expository strengths: the von Neumann-entropy section cleanly isolates the parallel-repetition mechanism, the parameter choices are explicit, and the admission that the key rate is coupled to the security parameter is an honest statement of a real limitation. However, the significance is conditional: the one-shot proof rests on Theorem 7.2 from the companion paper [MD24b], whose proof is not included, and on an asserted extension of several results from [BVY21] to the three-party setting with Eve's register, which is described only as instructions in Appendix B.

major comments (3)
  1. [§7.1, Theorem 7.2] The central one-shot entropy bound, Eq. (112), and hence the final key-rate bound, Eq. (118), are direct applications of Theorem 7.2, which is stated but not proved in this manuscript; the proof is relegated to the companion paper [MD24b]. Since Theorem 7.2 is the unstructured approximate entropy accumulation theorem that is doing the load-bearing work of converting the local approximation chain in Claim 7.3 into a global smooth min-entropy bound, the present manuscript is not self-contained on this point. A journal referee and a reader cannot verify the security claim without access to a proof of Theorem 7.2. Please either include a proof (or a detailed, verifiable derivation) of Theorem 7.2, or make the dependency completely explicit and ensure that the companion result is available and correct.
  2. [Appendix B, esp. items 5–9] The adaptation of [BVY21] to the three-party setting with Eve's register is asserted rather than proved. In particular, the manuscript states that Claims 5.13–5.16 go through by replacing E_A by E_AE and E_B by E_BE, that symmetry is unnecessary, and that the event W_C can be replaced by the trivial event; but no modified proofs are supplied. This matters because Proposition 5.1, stated as Eq. (36), is the unique bridge from the parallel n-fold 3CHSH⊥ strategy to a single-round strategy, and it is used in Lemma 6.5, Claim 7.3, and every subsequent entropy bound. If the O(δ^{1/16}/α^3) approximation in Eq. (36) relies on the conditioning event W_C in a way that fails when W_C is made trivial, or if the concentration step used to make P_{R_{-i}X_iY_i} close to P_{R_{-i}}P_{XY} uses the winning condition, then Lemma 6.5 and the unstructured EAT application lose their justification. The manuscript needs to provide the actual adapted proofs, not only a list of replacement instructions.
  3. [§6.1, Lemma 6.4] Lemma 6.4 is the step that shows the real protocol state ρ and the auxiliary state θ are close, and it is an input to Lemma 6.5. Its proof, however, contains a visibly corrupted display (the first line of the trace-norm computation) and then appeals to 'the equation after Eq. 88 in [BVY21] (setting W_C to be the trivial event)' without stating the equation or proving that the trivial-event specialization is valid. Since the entire simulation chain in Lemma 6.5, Claim 7.3, and Section 7.2 depends on this specific bound, this gap is load-bearing. Please supply a complete, self-contained proof of Lemma 6.4, including the derivation of the O(δ^{1/2}/α^2) bound in the three-party setting with Eve's register.
minor comments (4)
  1. [§6.1, around Eq. (43)] There is a notation inconsistency in the reduction step: the claim is written with H(A_{I_k}|EΩ^n_1 A_{i_1}⋯A_{i_{k-1}} I_j)ρ, but the surrounding text and the following formula indicate that the conditioning should be on I_k, not I_j. Please correct this.
  2. [Appendix C, Eqs. (136) and (145)] The notation F_{α,ν} is used inconsistently: in Eq. (107), F_{α,ν}(x) is defined to include the prefactor (1−α), so the expressions t((1−α)F_{α,ν}(ωth)−…) in Eqs. (136) and (145) appear to double-count the factor (1−α), whereas Eq. (112) writes the correct form t((1−α)F(g_{α,ν}(ωth))−…). Please clarify the intended definition or adjust the formulas.
  3. [§7.2, after Eq. (112)] The theorem application should explicitly state how the event ¬F (equivalently freq(W^t_1)(1) ≥ γωth) satisfies the min-tradeoff condition f(freq(x^n_1)) ≥ h in Theorem 7.2. This is implicit in the definition of F_{α,ν} and the choice of slope at γωth, but making the correspondence explicit would aid readability.
  4. [General] Several displayed equations in the manuscript contain OCR-like artifacts (for example, the first line of the proof of Lemma 6.4 and a few parenthetical references near Eq. (131)); these should be restored from the source file so that the proofs are actually readable.

Circularity Check

1 steps flagged · score 4.0 of 10

Central smooth min-entropy bound is imported from the authors' companion unstructured-EAT theorem; otherwise the derivation is not circular.

  1. self citation load bearing [Section 7.1 (Theorem 7.2) and Section 7.2 (Eq. 112), used in Appendix C.5 (Eq. 118)]
    "To address this need, we developed an unstructured approximate entropy accumulation theorem in our companion paper [MD24b]. ... Finally, applying the approximate EAT to the state ρ as described above, we get that ... H µ′+ϵ′ min ( ˆAt 1 ˆBt 1| ˆX t 1 ˆY t 1 T t 1I t 1ΩJ cE)ρ∣¬F ≥ t((1−α)F (gα,ν(ωth))− O( √µ νγ ))− O(1) (112)."

    The paper's advertised result, the positive key-rate bound of Eq. 118, is obtained by feeding the approximation Claim 7.3 into Theorem 7.2. Theorem 7.2 is not proved in this manuscript; it is quoted from the authors' own companion paper [MD24b]. Consequently the central smooth min-entropy lower bound, Eq. 112, is not derived here but is the direct output of a self-cited black box, and every later entropy statement inherits that dependence. This is load-bearing self-citation: if Theorem 7.2 were unavailable or invalid, Eq. 112 and Eq. 118 would collapse.

full rationale

No fully circular step was found beyond the load-bearing self-citation of the unstructured approximate EAT. The single-round 3CHSH⊥ entropy bound (Lemma 2.3) is derived from the external results [PAB+09, AF20]; the anchored parallel-repetition approximation (Proposition 5.1) is imported from the external work [BVY21]; and the protocol parameters (α, ν, γ, δ, t) are chosen, not fitted to the target entropy. The Appendix B adaptation of [BVY21] statements to the tripartite setting is asserted rather than fully demonstrated, and the proof of Theorem 7.2 is outsourced to a companion preprint; both are significant verification gaps, but neither is an equation-by-construction reduction of the claimed conclusion to its inputs. The central claim therefore retains independent content via the simulation argument in Box 1/Box 2, so the circularity score is 4 rather than higher.

Assumptions & free parameters 6 free parameters · 5 assumptions · 0 invented entities

The proof rests on two external pillars: the anchored parallel repetition machinery of [BVY21] and the unstructured approximate EAT from the authors' companion work [MD24b]. The former is prior work by other authors; the latter is self-cited and not proven here. The protocol parameters (alpha, nu, delta, gamma, omega_th, delta_1) are hand-chosen and couple the key rate to the security parameter. No new physical entities are introduced.

free parameters (6)
  • alpha (anchoring probability) = not fitted, chosen e.g. 10^-3
    Parameter of the 3CHSH⊥ game; selected in (0,0.1) and later fixed to make the key-rate bound positive. Affects both rate and security parameter.
  • nu (3CHSH question distribution parameter) = not fitted, chosen 10^-3
    Controls the probability of the CHSH-type questions; appears in the single-round entropy bound and the min-tradeoff function.
  • delta (subset fraction) = not fitted, chosen small
    Determines test subset size t and enters the approximation error O(delta^{1/16}/alpha^3) and EAT mu. Smaller delta improves security but reduces rate.
  • gamma (testing probability) = not fitted, chosen 10^-3
    Probability each raw-key round is used for testing; enters the leakage term 2 log|A| gamma and EAT bounds.
  • omega_th (winning threshold) = chosen so g_{alpha,nu}(omega_th) is about 0.84
    Threshold for not aborting; chosen near the CHSH quantum winning value so F >= 3/4 while remaining implementable.
  • delta_1 (small auxiliary parameter) = not fitted, chosen 10^-3
    Appears in Chernoff-bound events E1-E3 and max-entropy bound.
assumptions (5)
  • ad hoc to paper The unstructured approximate entropy accumulation theorem (Theorem 7.2) from [MD24b] holds as stated.
    Central one-shot tool, stated in full but proof deferred to companion work by the same authors; the security proof depends on it.
  • domain assumption The results of [BVY21], in particular Proposition 5.1, extend to the setting with Eve's register E and a non-symmetric state after the modifications listed in Appendix B.
    Appendix B asserts the extension without full derivations; the single-round simulation (Lemma 6.5) depends on it.
  • domain assumption The measurement devices of Alice and Bob are non-communicating and were prepared by Eve before the protocol; the device is used once on the joint input.
    Standard DIQKD assumption, stated in Section 1 and used in the state model Eq. 17.
  • domain assumption The seed distribution P_OmegaXY extension from [BVY21] exists and can be sampled efficiently (Eq. 15-16 and after).
    Protocol relies on Alice and Bob sampling questions from the anchored game via Omega.
  • standard math Standard quantum information background: purified distance, leftover hashing lemma, chain rules for smooth entropies, and the AFW continuity bound.
    Used throughout; cited to standard references.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Security proof for parallel DIQKD." pith.science (2026). https://pith.science/paper/WJC5ZV2D

@misc{pith2026250703991,
  author       = {Pith},
  title        = {Pith review of: Security proof for parallel DIQKD},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/WJC5ZV2D}},
  note         = {Machine review of arXiv:2507.03991}
}
read the original abstract

We present a parallel device independent quantum key distribution (DIQKD) protocol based on the CHSH game and prove its security. Using techniques developed for analysing the parallel repetition of anchored non-local games, we show that the answers on a small random linear subset of the games in the DIQKD protocol can be simulated as the output of a single-round strategy for playing the CHSH game. Then, we use the recently developed unstructured approximate entropy accumulation theorem to establish the smooth min-entropy lower bound required for the security proof. Our approach yields a more information-theoretic and general proof for parallel DIQKD compared to previous proofs.

Figures

Figures reproduced from arXiv: 2507.03991 by the authors.

Figure 1
Figure 1. The setting for entropy accumulation. The channels [PITH_FULL_IMAGE:figures/full_fig_p028_1.png] view at source ↗

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Parallel repetition of expanded, and multiplayer, Quantum games: anchoring, optimal values, generalized error bounds, dependency-breaking as symmetry-breaking

    quant-ph 2025-08 reject novelty 4.0 of 10

    States exponential decay bounds for the anchored parallel-repeated value of multiplayer quantum games with N-dependent exponents, but leaves the N-player proof to prior work.

Reference graph

Works this paper leans on

43 extracted references · 42 canonical work pages · cited by 1 Pith paper

  1. [1]

    Continuity of quantum conditional information

    R Alicki and M Fannes. Continuity of quantum conditional information. Journal of Physics A: Mathematical and General , 37(5):L55–L57, Jan 2004

    work page 2004

  2. [2]

    Device-Independent Quantum Information Processing

    Rotem Arnon-Friedman. Device-Independent Quantum Information Processing . Springer International Publishing, 2020

    work page 2020

  3. [3]

    Practical device-independent quantum cryptography via entropy accumulation

    Rotem Arnon-Friedman, Fr \'e d \'e ric Dupuis, Omar Fawzi, Renato Renner, and Thomas Vidick. Practical device-independent quantum cryptography via entropy accumulation. Nature Communications , 9(1):459, 2018

    work page 2018

  4. [4]

    Simple and tight device-independent security proofs

    Rotem Arnon-Friedman, Renato Renner, and Thomas Vidick. Simple and tight device-independent security proofs. SIAM Journal on Computing , 48(1):181--225, jan 2019

    work page 2019

  5. [5]

    Bennett and Gilles Brassard

    Charles H. Bennett and Gilles Brassard. Quantum cryptography: Public key distribution and coin tossing. Proceedings of the International Conference on Computers, Systems & Signal Processing, Bangalore, India , pages 175--179, 1984

    work page 1984

  6. [6]

    Charles H. Bennett. Quantum cryptography using any two nonorthogonal states. Phys. Rev. Lett. , 68:3121--3124, May 1992

    work page 1992

  7. [7]

    Computing conditional entropies for quantum correlations

    Peter Brown, Hamza Fawzi, and Omar Fawzi. Computing conditional entropies for quantum correlations. Nature Communications , 12(1):575, 2021

    work page 2021

  8. [8]

    No signaling and quantum key distribution

    Jonathan Barrett, Lucien Hardy, and Adrian Kent. No signaling and quantum key distribution. Phys. Rev. Lett. , 95:010503, Jun 2005

    work page 2005

Show all 43 references
  1. [9]

    Secret-key reconciliation by public discussion

    Gilles Brassard and Louis Salvail. Secret-key reconciliation by public discussion. In Tor Helleseth, editor, Advances in Cryptology --- EUROCRYPT '93 , pages 410--423, Berlin, Heidelberg, 1994. Springer Berlin Heidelberg

    1994

  2. [10]

    Anchored parallel repetition for nonlocal games, 2021

    Mohammad Bavarian, Thomas Vidick, and Henry Yuen. Anchored parallel repetition for nonlocal games, 2021

    2021

  3. [11]

    Clauser, Michael A

    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, Oct 1969

    1969

  4. [12]

    Parallel repetition of entangled games with exponential decay via the superposed information cost

    Andr \'e Chailloux and Giannicola Scarpa. Parallel repetition of entangled games with exponential decay via the superposed information cost. In Javier Esparza, Pierre Fraigniaud, Thore Husfeldt, and Elias Koutsoupias, editors, Automata, Languages, and Programming , pages 296--...

    2014

  5. [13]

    Perfect parallel repetition theorem for quantum xor proof systems

    Richard Cleve, William Slofstra, Falk Unger, and Sarvagya Upadhyay. Perfect parallel repetition theorem for quantum xor proof systems. computational complexity , 17(2):282--299, 2008

    2008

  6. [14]

    Parallel repetition for entangled player games via fast quantum search

    Kai-Min Chung, Xiaodi Wu, and Henry Yuen. Parallel repetition for entangled player games via fast quantum search. In Proceedings of the 30th Conference on Computational Complexity , CCC '15, page 512–536, Dagstuhl, DEU, 2015. Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik

    2015

  7. [15]

    Entropy accumulation

    Fr\'ed\'eric Dupuis, Omar Fawzi, and Renato Renner. Entropy accumulation. Communications in Mathematical Physics , 379(3):867--913, 2020

    2020

  8. [16]

    A parallel repetition theorem for entangled projection games

    Irit Dinur, David Steurer, and Thomas Vidick. A parallel repetition theorem for entangled projection games. In Proceedings of the 2014 IEEE 29th Conference on Computational Complexity , CCC '14, page 197–208, USA, 2014. IEEE Computer Society

    2014

  9. [17]

    Artur K. Ekert. Quantum cryptography based on bell's theorem. Phys. Rev. Lett. , 67:661--663, Aug 1991

    1991

  10. [18]

    Parallel repetition: Simplifications and the no-signaling case

    Thomas Holenstein. Parallel repetition: Simplifications and the no-signaling case. Theory of Computing , 5(1):141--172, 2009

    2009

  11. [19]

    A direct product theorem for quantum communication complexity with applications to device-independent qkd

    Rahul Jain and Srijita Kundu. A direct product theorem for quantum communication complexity with applications to device-independent qkd. In 2021 IEEE 62nd Annual Symposium on Foundations of Computer Science (FOCS) , pages 1285--1295, 2022

    2021

  12. [20]

    Jain , C

    R. Jain , C. A. Miller , and Y. Shi . Parallel device-independent quantum key distribution. IEEE Transactions on Information Theory , 66(9):5567--5584, 2020

    2020

  13. [21]

    A parallel repetition theorem for entangled two-player one-round games under product distributions

    Rahul Jain, Attila Pereszl\'enyi, and Penghui Yao. A parallel repetition theorem for entangled two-player one-round games under product distributions. In 2014 IEEE 29th Conference on Computational Complexity (CCC) , pages 209--216, 2014

    2014

  14. [22]

    Entangled games are hard to approximate

    Julia Kempe, Hirotada Kobayashi, Keiji Matsumoto, Ben Toner, and Thomas Vidick. Entangled games are hard to approximate. 2008 49th Annual IEEE Symposium on Foundations of Computer Science , pages 447--456, 2008

    2008

  15. [23]

    Hacking commercial quantum cryptography systems by tailored bright illumination

    Lars Lydersen, Carlos Wiechers, Christoffer Wittmann, Dominique Elser, Johannes Skaar, and Vadim Makarov. Hacking commercial quantum cryptography systems by tailored bright illumination. Nature Photonics , 4(10):686--689, 2010

    2010

  16. [24]

    Masanes, A

    Ll. Masanes, A. Acin, and N. Gisin. General properties of nonsignaling theories. Phys. Rev. A , 73:012112, Jan 2006

    2006

  17. [25]

    Smooth min-entropy lower bounds for approximation chains

    Ashutosh Marwah and Fr \'e d \'e ric Dupuis. Smooth min-entropy lower bounds for approximation chains. Communications in Mathematical Physics , 405(9):211, 2024

    2024

  18. [26]

    Universal chain rules from entropic triangle inequalities, 2024

    Ashutosh Marwah and Frédéric Dupuis. Universal chain rules from entropic triangle inequalities, 2024

    2024

  19. [27]

    Generalised entropy accumulation

    Tony Metger, Omar Fawzi, David Sutter, and Renato Renner. Generalised entropy accumulation. Communications in Mathematical Physics , 405(11):261, 2024

    2024

  20. [28]

    Miller and Yaoyun Shi

    Carl A. Miller and Yaoyun Shi. Randomness in nonlocal games between mistrustful players. Quantum information & computation , 17 7:595--610, 2017

    2017

  21. [29]

    Self testing quantum apparatus

    Dominic Mayers and Andrew Yao. Self testing quantum apparatus. Quantum Info. Comput. , 4(4):273–286, July 2004

    2004

  22. [30]

    Device-independent quantum key distribution secure against collective attacks

    Stefano Pironio, Antonio Ac\'in, Nicolas Brunner, Nicolas Gisin, Serge Massar, and Valerio Scarani. Device-independent quantum key distribution secure against collective attacks. New Journal of Physics , 11(4):045021, Apr 2009

    2009

  23. [31]

    Cryptographic security of quantum key distribution, 2014

    Christopher Portmann and Renato Renner. Cryptographic security of quantum key distribution, 2014

    2014

  24. [32]

    A parallel repetition theorem

    Ran Raz. A parallel repetition theorem. SIAM Journal on Computing , 27(3):763--803, 1998

    1998

  25. [33]

    Security of Quantum Key Distribution

    Renato Renner. Security of Quantum Key Distribution . PhD thesis, 2006

    2006

  26. [34]

    Universally composable privacy amplification against quantum adversaries

    Renato Renner and Robert K \"o nig. Universally composable privacy amplification against quantum adversaries. In Joe Kilian, editor, Theory of Cryptography , pages 407--425, Berlin, Heidelberg, 2005. Springer Berlin Heidelberg

    2005

  27. [35]

    Shor and John Preskill

    Peter W. Shor and John Preskill. Simple proof of security of the BB84 quantum key distribution protocol. Phys. Rev. Lett. , 85:441--444, Jul 2000

    2000

  28. [36]

    Attacks exploiting deviation of mean photon number in quantum key distribution and coin tossing

    Shihan Sajeed, Igor Radchenko, Sarah Kaiser, Jean-Philippe Bourgoin, Anna Pappa, Laurent Monat, Matthieu Legr\'e, and Vadim Makarov. Attacks exploiting deviation of mean photon number in quantum key distribution and coin tossing. Phys. Rev. A , 91:032326, Mar 2015

    2015

  29. [37]

    A largely self-contained and complete security proof for quantum key distribution

    Marco Tomamichel and Anthony Leverrier. A largely self-contained and complete security proof for quantum key distribution. Quantum , 1:14, July 2017

    2017

  30. [38]

    Quantum Information Processing with Finite Resources

    Marco Tomamichel. Quantum Information Processing with Finite Resources . Springer International Publishing, 2016

    2016

  31. [39]

    Leftover hashing against quantum side information

    Marco Tomamichel, Renato Renner, Christian Schaffner, and Adam Smith. Leftover hashing against quantum side information. In IEEE International Symposium on Information Theory , pages 2703 --2707, June 2010

    2010

  32. [40]

    Chain rules for smooth min- and max-entropies

    Alexander Vitanov, Fr\'ed\'eric Dupuis, Marco Tomamichel, and Renato Renner. Chain rules for smooth min- and max-entropies. IEEE Transactions on Information Theory , 59(5):2603--2612, 2013

    2013

  33. [41]

    Parallel DIQKD from parallel repetition, 2017

    Thomas Vidick. Parallel DIQKD from parallel repetition, 2017

    2017

  34. [42]

    Tight uniform continuity bounds for quantum entropies: Conditional entropy, relative entropy distance and energy constraints

    Andreas Winter. Tight uniform continuity bounds for quantum entropies: Conditional entropy, relative entropy distance and energy constraints. Communications in Mathematical Physics , 347(1):291--313, 2016

    2016

  35. [43]

    A parallel repetition theorem for all entangled games, 2016

    Henry Yuen. A parallel repetition theorem for all entangled games, 2016

    2016

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.