Paper · P01

Optimal counterfeiting attacks and generalizations for Wiesner's quantum money

Title from docs/planning/QMINT_MASTER_RESEARCH_PLAN.md section 16; not present in the matrix row.

Abel Molina; Thomas Vidick; John Watrous · 2012-02-17 (arXiv v1)

Status: FULL TEXT READLane A read the full text of the primary source.FULL_TEXT_READ (abs page + arXiv PDF v1, 18 pp)
Game: W1 W1_CV
Anchor: —
Source file: research/PRIOR_ART_MATRIX.csv

Precise theorem

Thm 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 from one ticket) succeeds with probability exactly (3/4+sqrt(2)/8)^n. Sec 3.5 eq.(4): binomial-tail bound for a joint-threshold variant (see THEOREM_REGISTRY_SEED T-MVW12-SEC35).

Citations

https://arxiv.org/abs/1202.4010(opens in a new tab)

Record

Every field of the source record, in file order.

Canonical linkcanonical_link: https://arxiv.org/abs/1202.4010
Authorsauthors: Abel Molina; Thomas Vidick; John Watrous
Publication datepublication_date: 2012-02-17 (arXiv v1)
Versionversion: arXiv v1 is the only arXiv version (submission history checked 2026-10-11). Conference version (TQC 2012, LNCS) NOT_VERIFIED - not fetched.
Correction statuscorrection_status: No erratum found on arXiv page; journal/conference erratum not checked (NOT_VERIFIED).
Input modelinput_model: Bank prepares n qubits, each uniformly from {|0>,|1>,|+>,|->}; secret key k kept by bank; unique serial number; ideal noiseless states.
Verifier modelverifier_model: W1: bank applies projective measurement {Pi=|psi_k><psi_k|, 1-Pi} on each returned note (exact, accept-all-qubits). W1_CV: bank sends uniformly random challenge c in {0,1}^n, user measures qubit i in Z if c_i=0 or X if c_i=1; bank accepts iff all outcomes in matching-basis positions are correct; verification destroys the ticket.
Adversary capabilitiesadversary_capabilities: Arbitrary CPTP channel from one note register X to two registers (Y,Z) (W1), or arbitrary POVM depending on both challenges (c1,c2) (W1_CV). NO additional access to the bank's verifier (no adaptive verification queries); single note; independent verification of both outputs.
Tested parameterstested_parameters: Analytic; n arbitrary. n=1 SDP optimum 3/4 with explicit primal (Kraus A0,A1 p.8) and dual Y=(3/8)I. Also: 6-state/SIC ensembles -> (2/3)^n; d-dim 3-design -> 2/(d+1); qudit classical verification -> (3/4+1/(4 sqrt d))^n.
Proof dependenciesproof_dependencies: SDP duality (Slater, Thm 3); Choi-Jamiolkowski; product property of SDPs with PSD objective (Mittal-Szegedy) for n-fold repetition (Sec 3.4).
Datasetsdatasets: none
Codecode: none released (paper mentions CVX used during research; not published)
Licenselicense: arXiv non-exclusive distribution licence 1.0 (paper text). No code.
Limitationslimitations: Only 'simple counterfeiting' (1 note -> 2 notes, no verifier interaction). Paper explicitly notes other attacks exist (e.g. 2^-n Bell-state attack with verifier interaction; Lutomirski O(n) attack when post-verification qubits are returned). Ideal states/verifier; no loss/noise in Thm 1/2.
What QMint addswhat_QMint_adds: Nothing new theoretically. QMint may reproduce Thm 1 (n=1 SDP + analytic n) as an L1 reproduction and use it as a golden test for game W1 only.
Access statusaccess_status: FULL_TEXT_READ (abs page + arXiv PDF v1, 18 pp)
Qmint gameqmint_game: W1; W1_CV

Citations

Record

Related entries