Library
Research library
Papers, transcribed theorems, proof obligations, datasets, corrections and the novelty audit, read directly from the lane A, D and E files in this repository. Each entry keeps the verification status written in its own file; nothing here is upgraded or merged by the website.
81 of 81 entries
Papers24
- P01FULL TEXT READOptimal counterfeiting attacks and generalizations for Wiesner's quantum moneyThm 1 (p.2): optimal simple counterfeiting attack on Wiesner's n-qubit scheme succeeds with probability exactly (3/4)^n. Thm 2 (p.3) / Lemma 5 (p.14): classical-verification variant, optimal simple counterfeiting attack (two independent challenges answered fr…W1 · W1_CV2012FULL TEXT READ
- P02FULL TEXT READS-money: virtual tokens for a relativistic economyNo numbered quantitative unforgeability theorem.S1 · S22019doi:10.1098/rspa.2019.0170FULL TEXT READ
- P03FULL TEXT READPractical quantum tokens without quantum memories and experimental testsLemma 1 (eq.1): ideal IQT1/IQT2 eps_unf=(1/2+1/(2 sqrt2))^N. Lemma 2 (eqs 2-3) robustness; Lemma 3 (eqs 4-5) correctness; Lemma 4 (eq 6) eps_priv=beta_E; Theorem 1 (eqs 7-10) realistic unforgeability eps_unf = exp(-Pnoqub N/3 (nu_unf/Pnoqub-1)^2) + exp(-N f(.…S1 · S22022doi:10.1038/s41534-022-00524-4FULL TEXT READ
- P04FULL TEXT READDemonstration of quantum-digital paymentsNo numbered theorem.D12023doi:10.1038/s41467-023-39519-wFULL TEXT READ
- P05FULL TEXT READExperimental practical quantum tokens with transaction time advantageTheorem 1 (eqs 23-25, Methods p.~17): eps_unf = sum_{l=0}^{floor(N(1-nu_unf))} C(N,l)(1-Pnoqub,theta)^l Pnoqub,theta^{N-l} + sum_{l=0}^{floor(n gamma_err)} C(n-floor(N nu_unf), l)(1-Pbound)^l Pbound^{n-floor(N nu_unf)-l}, under max 2 P_MC(chi) <= Pbound < 1 e…S22024FULL TEXT READ
- P06ABSTRACT READAnonymous Quantum Tokens with Classical VerificationDefinition 9 (tokens with classical verification, parameters n,m,N_Mint,N_Verify,t,eps_loss,eps_fraud); Construction 10 meets Def.9 with n=k, m=k 2^{k/4}, N_Mint=2^{k/4}, N_Verify=2^{k/2}, t=k, eps_loss=2^{-k/2}, eps_fraud=2^{-k/4} (4|k); Definition 11 repeti…A12025ABSTRACT READ
- P07ABSTRACT READPractical quantum tokens: challenges and perspectivesPerspective article; no new security theorem.2026doi:10.1088/2058-9565/ae92adABSTRACT READ
- P08ABSTRACT READQuantum Money from Abelian Group ActionsPublic-key quantum money / quantum lightning from abelian group actions; security proved in the generic group model for group actions under a plausible computational assumption (abstract).2023doi:10.46298/theoretics.25.18ABSTRACT READ
- P09ABSTRACT READCryptanalysis of Three Quantum Money SchemesPolynomial-time quantum algorithm for the Aaronson-Christiano hidden-subspace hard problem; polynomial-time cloning attack on Zhandry 2017 multivariate-hash money; reduction for Kane-Sharif-Silverberg quaternion scheme (abstract).2022ABSTRACT READ
- P10ABSTRACT READAnonymous Public-Key Quantum Money and Quantum VotingAssuming iO and LWE: public-key quantum money with anonymity against users and traceability by authorities, and an untraceable variant; universally verifiable quantum voting (abstract).2024ABSTRACT READ
- P11ABSTRACT READYuen (2024)Noise-tolerant public-key quantum money in the Aaronson-Christiano classical-oracle model (abstract).2024doi:10.22331/q-2025-04-07-1691ABSTRACT READ
- P12ABSTRACT READDoliskani, Mirzaei & Mousavi (2025)Public-key quantum money from group actions + quantum Hartley transform (adapts Zhandry 2024); new verification with group-action twists; recursive QHT (abstract).2025ABSTRACT READ
- P13METADATA ONLYPastawski et al. (2012)Noise-tolerant quantum tokens with threshold verification; tight (2/3)^n for 6-state variant per MVW's summary (P01 p.4).W22012doi:10.1073/pnas.1203552109METADATA ONLY
- P14METADATA ONLYBozzio et al. (2018)Experimental investigation of practical unforgeable quantum money (classical-verification, weak coherent states).W1_CV2018doi:10.1038/s41534-018-0058-2METADATA ONLY
- P15METADATA ONLYBozzio, Diamanti & Grosshans (2019)Semi-device-independent quantum money with coherent states; SDP that simultaneously optimises over noise and losses introduced by a dishonest party (per search snippet; NOT transcribed).D12019doi:10.1103/PhysRevA.99.022336METADATA ONLY
- P16METADATA ONLYKent & Pitalúa-García (2019)Flexible quantum tokens in spacetime (ref 28 of P03).S1 · S22019METADATA ONLY
- P17ABSTRACT READMamann et al. (2025)Experimental Wiesner quantum-money primitive with an intermediate cold-atom quantum-memory storage step; 'stringent requirements on storage efficiency and noise level to reach a secure regime' (abstract).W1 · W22025doi:10.1126/sciadv.adx3223ABSTRACT READ
- P18METADATA ONLYBozzio et al. (2025)Review: quantum cryptography beyond QKD (incl. quantum money/tokens).2025doi:10.1103/p84v-1xqvMETADATA ONLY
- P19METADATA ONLYWinick, Lütkenhaus & Coles (2018)Reliable (lower-bound) numerical QKD key rates via two-step SDP with dual certificate; openQKDsecurity implements protocol-generic numerical key rates and parameter optimisation (per repo/search).2018doi:10.22331/q-2018-07-26-77METADATA ONLY
- P20METADATA ONLYBunandar et al. (2020)Numerical finite-key analysis of QKD as SDPs (per search snippet).2020doi:10.1038/s41534-020-00322-wMETADATA ONLY
- P21METADATA ONLYWang & Lo (2019)Machine learning (neural network) prediction of optimal QKD protocol parameters (title/metadata).2019doi:10.1103/PhysRevA.100.062334METADATA ONLY
- P22METADATA ONLYChung, Ng & Cai (2025)Generalised numerical framework for finite-size QKD key rates with Rényi entropy (builds on openQKDsecurity per search snippet).2025doi:10.1103/tyts-8v8jMETADATA ONLY
- P23ABSTRACT READGenovese & Stambler (2025)Publicly verifiable quantum money with limited verifications from one-time memories (conjugate coding + hardware assumptions) (abstract).2025ABSTRACT READ
- P24ABSTRACT READDasari, Wang & Wrachtrup (2026)Proposal: spin-photon interfaces (NV/diamond) to secure preparation, storage and verification stages of quantum token protocols (abstract).2026ABSTRACT READ
Theorems15
- T-MVW12-THM1VERIFIED FROM SOURCEMolina, Vidick & Watrous 2012 · Theorem 1Theorem 1. The optimal simple counterfeiting attack against Wiesner's quantum money scheme has success probability exactly (3/4)^n, where n is the number of qubits in each bank note.W1VERIFIED FROM SOURCE
- T-MVW12-THM2VERIFIED FROM SOURCEMolina, Vidick & Watrous 2012 · Theorem 2Theorem 2. For the classical-verification analogue of Wiesner's quantum money scheme, the optimal simple counterfeiting attack has success probability exactly (3/4 + sqrt(2)/8)^n, for n being the number of qubits in each bank note.W1_CVVERIFIED FROM SOURCE
- T-MVW12-SEC35VERIFIED FROM SOURCEMolina, Vidick & Watrous 2012 · Sec. 3.5 'Threshold results'For n-fold repetition where the bank declares the note valid when at least t of n repetitions succeed, the optimal counterfeiting probability equals sum_{t<=j<=n} C(n,j) alpha^j (1-alpha)^{n-j} (eq. 4), with alpha the single-repetition optimum (3/4 for Wiesne…W1_THRESH_JOINTVERIFIED FROM SOURCE
- T-KLPR22-LEMMA1VERIFIED FROM SOURCEKent et al. 2022 · Lemma 1Lemma 1: The quantum token schemes IQT1 and IQT2 are eps_unf-unforgeable with eps_unf = (1/2 + 1/(2 sqrt 2))^N.S1doi:10.1038/s41534-022-00524-4VERIFIED FROM SOURCE
- T-KLPR22-LEMMA2VERIFIED FROM SOURCEKent et al. 2022 · Lemma 2If 0 < gamma_det < P_det (2), then QT1 and QT2 are eps_rob-robust with (3).S2doi:10.1038/s41534-022-00524-4VERIFIED FROM SOURCE
- T-KLPR22-LEMMA3VERIFIED FROM SOURCEKent et al. 2022 · Lemma 3If (4) holds, QT1 and QT2 are eps_cor-correct with (5).S2doi:10.1038/s41534-022-00524-4VERIFIED FROM SOURCE
- T-KLPR22-LEMMA4VERIFIED FROM SOURCEKent et al. 2022 · Lemma 4QT1 and QT2 are eps_priv-private with eps_priv = beta_E.S2doi:10.1038/s41534-022-00524-4VERIFIED FROM SOURCE
- T-KLPR22-THM1VERIFIED FROM SOURCEKent et al. 2022 · Theorem 1Consider constraints (7) and define f by (8)-(9).S2doi:10.1038/s41534-022-00524-4VERIFIED FROM SOURCE
- T-KLPR22-THM2VERIFIED FROM SOURCEKent et al. 2022 · Theorem 2For any integer M >= 1 there exist schemes QT1^M, QT2^M (2^M presentation points, Bob sends NM states) that, under constraints (2), (4), (7) with f > 0, have the parameters below.S2doi:10.1038/s41534-022-00524-4VERIFIED FROM SOURCE
- T-KLPR22-LEMMA5VERIFIED FROM SOURCEKent et al. 2022 · MethodsUnder assumptions E and F, reporting strategy 1 (QT1) and 2 (QT2) give report probabilities that factorise over pulses and don't depend on the measured basis.S2doi:10.1038/s41534-022-00524-4VERIFIED FROM SOURCE
- T-SCH23-SDP-N1VERIFIED FROM SOURCESchiansky et al. 2023 · Supplementary InformationTwo-merchant double-spend: from the token state rho_P produce two classical cryptograms kappa_0 (Z basis, M0) and kappa_1 (X basis, M1) that both pass.D1doi:10.1038/s41467-023-39519-wVERIFIED FROM SOURCE
- T-SCH23-ASYMPTOTICVERIFIED FROM SOURCESchiansky et al. 2023 · Supplementary Note 3BAnalytic fit to the optimal cheating boundary: e = -(1/(4+2 sqrt2)) l + (1 - p_m/2)/(8 + 4 sqrt2) (16).D1doi:10.1038/s41467-023-39519-wVERIFIED FROM SOURCE
- T-SCH23-FINITEVERIFIED FROM SOURCESchiansky et al. 2023 · Supplementary Note 3CHonest success p_h >= 1 - exp(-(delta_h^2/3) M(e_h,l_h) N) (20), subject to M(e_h,l_h)(1+delta_h) < (1/2)(1-p_m/2) (21).D1doi:10.1038/s41467-023-39519-wVERIFIED FROM SOURCE
- T-JIANG24-THM1VERIFIED FROM SOURCEJiang et al. 2024 · Methods 'Security analysis'If max_{j,k} 2 P_MC(chi^k_j) < 1, N gamma_det <= n <= N, and 0 < P_noqub,theta < nu_unf < gamma_det (1 - gamma_err/(1 - P_bound)), with max 2 P_MC <= P_bound < 1, then eps_unf = sum_{l=0}^{floor(N(1-nu_unf))} C(N,l)(1-P_noqub,theta)^l P_noqub,theta^{N-l} + su…S2_JIANG24VERIFIED FROM SOURCE
- T-GAV25-CONSTR10NOT VERIFIEDGavinsky et al. 2025 · Definition 9Construction 10 satisfies Definition 9 with n = k, m = k 2^{k/4}, N_Mint = 2^{k/4}, N_Verify = 2^{k/2}, t = k, eps_loss = 2^{-k/2}, eps_fraud = 2^{-k/4}, for any 4 | k. Anonymity (Claim 13) is an audit bound via swap test.A1NOT VERIFIED
Proof obligations10
- P-W1PUBLISHED REPRODUCEDMVW2012 Theorem 1 (p.2)P_two_valid(n) = (3/4)^n (tight)W1PUBLISHED REPRODUCED
- P-W1CVPUBLISHED REPRODUCEDMVW2012 Theorem 2 (p.3)(3/4 + sqrt(2)/8)^n (tight)W1_CVPUBLISHED REPRODUCED
- P-W2CERTIFIED NUMERICPlan obligation: demonstrate the SDP construction and primal/dual consistency at n=1 (support, not an original proof).W1: 3/4 <= OPT_1 <= 0.750000000003638, 9/16 <= OPT_2 <= 0.562500000007276; W1_CV: OPT_1 <= 0.9267766955417756 (lane C).W2CERTIFIED NUMERIC
- P-S1PUBLISHED REPRODUCEDKLPR2022 Lemma 1, Eq. (1) (main text p.5; proof SI Note IV)(1/2 + 1/(2 sqrt 2))^NS1doi:10.1038/s41534-022-00524-4PUBLISHED REPRODUCED
- P-S2PUBLISHED REPRODUCEDKLPR2022 Lemmas 2,3,4 (Eqs. 2-6; proofs SI Note V), Theorem 1 (Eqs. 7-10; proof SI Note VII), Theorem 2 (Eq. 11; SI Not…eps_rob = exp(-(P_det N/2)(1 - gamma_det/P_det)^2) [Eq. 3, domain Eq. 2] eps_cor = exp(-(P_det(1-2b_PB)N/4)(1 - 2 nu_cor/(P_det(1-2b_PB)))^2) + exp(-(E nu_cor N/3)(gamma_err/E - 1)^2) [Eq. 5, domain Eq. 4] eps_priv = beta_E [Eq. 6] eps_unf = exp(-(P_noqub N/3…S2doi:10.1038/s41534-022-00524-4PUBLISHED REPRODUCED
- P-S3UNSUPPORTEDSpacetime/locality invariant of KLPR2022 Tables 1-3 (stage I in the intersection of the causal pasts of all Q_i; valida…none (invariant over simulated event DAGs)S1doi:10.1038/s41534-022-00524-4UNSUPPORTED
- P-D1NUMERICALLY SUPPORTEDSchiansky et al. 2023 SI Note 3p_d <= exp(-(delta_d^2/2) * (1/2)(1 - p_m/2) * N) [SI Eq. 22] 1 - p_h <= exp(-(delta_h^2/3) * M(e_h,l_h) * N), M = (4+2 sqrt 2) e + l [SI Eqs. 18-20] admissible iff (1/2)(1 - p_m/2)(1 - delta_d) >= M(e_h,l_h)(1 + delta_h) [SI Eq. 23]D1doi:10.1038/s41467-023-39519-wNUMERICALLY SUPPORTED
- P-C1UNSUPPORTEDSystems game, no cryptographic theoremnoneC1UNSUPPORTED
- P-OPTUNSUPPORTEDCompiler outputs satisfy previously certified constraints (every reported configuration re-checked by qmint.proofs.chec…noneUNSUPPORTED
- P-PRIVUNSUPPORTEDTranscribed bound: KLPR2022 Lemma 4 Eq. (6) and Eq. (11) (bound P-S2/priv).Pr[Bob guesses b] <= 2^-M + eps_priv^MS2doi:10.1038/s41534-022-00524-4UNSUPPORTED
Datasets6
- DS-SCH23-TIMETAGS-V1VERIFIED LISTINGData for Demonstration of quantum-digital paymentsTimetags that lead to coincidence count events in a 3ns window for Client and TTP, for linear (commitment to M0) and diagonal (M1) basis.2023doi:10.5281/zenodo.7979319VERIFIED LISTING
- DS-SCH23-TIMETAGS-V2VERIFIED LISTINGData for Demonstration of quantum-digital paymentsAdds: 'The files in folder "tagfile_example" are intended as input to the analysis scripts provided under DOI 10.5281/zenodo.7997961'.2023doi:10.5281/zenodo.7997998VERIFIED LISTING
- DS-SCH23-CODEVERIFIED DOWNLOADCode for Demonstration of quantum-digital paymentsDon't copy code into QMint.2023doi:10.5281/zenodo.8020667VERIFIED DOWNLOAD
- DS-RIPE-ATLASPARTIALLY VERIFIEDRIPE Atlas public measurements (REST API)BigQuery access can incur charges.PARTIALLY VERIFIED
- DS-KLPR22-PUBLISHED-PARAMSVERIFIED DOWNLOADKent et al. 2022 published experimental parameters (aggregate, not raw)P03 Results + Methods; see THEOREM_REGISTRY_SEED T-KLPR22-THM1.published_parameter_tuplesVERIFIED DOWNLOAD
- DS-JIANG24-PUBLISHED-PARAMSVERIFIED DOWNLOADJiang et al. 2024 published experimental parameters (aggregate, preprint)P05 arXiv v2 Methods; see THEOREM_REGISTRY_SEED T-JIANG24-THM1.reported_valuesVERIFIED DOWNLOAD
Corrections12
- CORR-P04PUBLISHED CORRECTIONPublished correction: P04 — Schiansky et al.Correction: Author Correction, published 21 August 2023, https://doi.org/10.1038/s41467-023-40866-x (Nat.doi:10.1038/s41467-023-40866-xPUBLISHED CORRECTION
- CORR-VERSIONSVERSION CHANGEDataset and code version changes (Zenodo)Zenodo data, concept 10.5281/zenodo.7979318: the paper cites v1 = 7979319 (153,143,236 B, md5 fd708578…bf94).D1doi:10.5281/zenodo.7979318:**VERSION CHANGE
- CORR-D-1OPEN DISCREPANCYMultiphoton probability 6.76±0.12 % (main) vs p_m = 6.02±0.28 % (SI)OPEN DISCREPANCY
- CORR-D-2OPEN DISCREPANCYSub-token length N = 4.2×10⁶ (Fig. 4b) vs 4 482 440 ± 1600 (SI Table 2)OPEN DISCREPANCY
- CORR-D-3OPEN DISCREPANCYChoi operator defined with 1/d prefactor but TP condition written as Tr_out J = 1 (should be (1/d)·1 under that normalisation)OPEN DISCREPANCY
- CORR-D-4OPEN DISCREPANCYDual variable X1 called "Hermitian 2×2", while the TP constraint lives on 7-dim H_POPEN DISCREPANCY
- CORR-D-5OPEN DISCREPANCYChernoff bounds stated for sums of independent {0,1} variables (with μ used both as per-trial mean and total).OPEN DISCREPANCY
- CORR-D-6OPEN DISCREPANCYReduction from coherent to i.i.d. attacks is a qualitative de Finetti argument with no finite-N correction termOPEN DISCREPANCY
- CORR-D-8OPEN DISCREPANCYReported ε′_cor = 2.1×10⁻¹¹, ε′_unf = 5.52×10⁻⁹OPEN DISCREPANCY
- CORR-D-9OPEN DISCREPANCYγ_err and ν_cor per plotted point aren't publishedOPEN DISCREPANCY
- CORR-D-10OPEN DISCREPANCYMissing find_start_alt module and requirements.txt.OPEN DISCREPANCY
- CORR-D-11RESOLVEDarXiv lists "Nature Communications 14, 3849 (2023)".RESOLVED
Novelty audit14
- NOV-H1HYPOTHESISH1 · Cross-protocol, game-typed certificate formatA machine-checkable certificate that ties every ε to a named game (W1, W1_CV, S1, S2, D1, …), a theorem ID with a source anchor, assumption flags (e.g. P03 Table 6 A–G), and an evidence kind.D1 · S1 · S2 · W1 · W1_CVHYPOTHESIS
- NOV-H2HYPOTHESISH2 · Systematic optimisation over published boundsTreat P03 Lemmas 2–3 + Thm 1 (and P04 eqs.(19)–(23), P05 Thm 1) as *fixed, cited* constraints and search the free parameters (γ_det, γ_err, ν_cor, ν_unf, N, δ_h, δ_d) to minimise resource cost at fixed ε. Report the gap against each paper's published tuple. *…HYPOTHESIS
- NOV-H3HYPOTHESISH3 · Uncertainty-aware calibration from public raw dataEstimate (e, l, p_m) intervals from the Zenodo timetags with time-blocked holdouts and drift stress.D1HYPOTHESIS
- NOV-H4HYPOTHESISH4 · Independent reproduction and consistency auditRe-derive P04's N=1 SDP and P01's SDP with residual accounting.HYPOTHESIS
- NOV-H5HYPOTHESISH5 · Falsification harnessPair every certified configuration with the best known *attack* (Monte Carlo lower bounds, SDP optima at small n) so certificates can be shown to be non-vacuous and to fail when they should.HYPOTHESIS
- NOV-H6HYPOTHESISH6 · Trust-matched quantum vs classical systems benchmarkCompare on matched topology/trust.HYPOTHESIS
- NOV-C1CONFLICTC1 · P03 already gives device-parameter → ε maps and a computed secure regionKent et al. 2022 Thm 1/Lemmas 2–3 are exactly "measured device parameters → certified ε", and Fig. 5 is a security region.CONFLICT
- NOV-C2CONFLICTC2 · P05 already propagates measurement confidence into ε and measured a time advantageJiang et al. 2024 eqs.(26)–(29) and the 2.77/60.54 km transaction-time result.CONFLICT
- NOV-C3CONFLICTC3 · P04/P15 already contain an SDP over noise and loss with a finite-N token-length selectionQMint can't claim a novel "loss-dependent attack SDP" or "first finite-size quantum-payment security curve from real data".CONFLICT
- NOV-C4CONFLICTC4 · QKD numerical-security tooling (P19–P22: openQKDsecurity, numerical_qkd, Rényi finite-size frameworks, ML parameter prediction)Generic "certified numerical bound + parameter optimisation from device data" is established in QKD.CONFLICT
- NOV-C5CONFLICTC5 · P01 Sec. 3.5 threshold result and P13 noise-tolerant tokensAny QMint "noise-tolerant Wiesner bound" risks duplicating (or misapplying) these.CONFLICT
- NOV-C6CONFLICTC6 · P17 (Mamann et al. 2025) derives a secure regime from measured quantum-memory efficiency/noise for Wiesner moneyThat conflicts with any "first experimental-data-driven Wiesner security region" claim.CONFLICT
- NOV-C7CONFLICTC7 · PatentsUS 10,790,972 (Kent, S-money style tokens, assigned to CQC/Quantinuum per Google Patents) and EP 23168897.9 (Univ.CONFLICT
- NOV-DISALLOWEDDISALLOWEDDisallowed false statements"QMint proves Wiesner money is secure with (3/4)^n." False framing.DISALLOWED