Proof obligation · P-W1
MVW2012 Theorem 1 (p.2)
wiesner_ideal · A. Molina, T. Vidick, J. Watrous. Optimal counterfeiting attacks and generalizations for Wiesner's quantum money. TQC 2012, LNCS 7582, 45-64. arXiv:1202.4010v1
- Status
- PUBLISHED REPRODUCEDLane D reproduced the published bound in code with an independent check.
- Game
- W1
- Anchor
- MVW2012 Theorem 1
- Source file
- proofs/OBLIGATIONS.yaml
Source and theorem
MVW2012 Theorem 1 (p.2): optimal simple counterfeiting attack on Wiesner's scheme succeeds with probability exactly (3/4)^n.
Citations
Record
Every field of the source record, in file order.
- Protocolprotocol
wiesner_ideal
- Gamegame
W1
- Sourcesource
MVW2012
- Assumptionsassumptions
- Bank note = n qubits, each uniformly and independently one of |0>,|1>,|+>,|-> (secret to the adversary).
- Adversary receives exactly ONE valid note and applies any quantum channel to output two notes (simple counterfeiting).
- No access to a verification oracle; no repeated or adaptive verification; no leaked post-measurement states (MVW2012 p.2 explicitly excludes these).
- Bank verifies each candidate independently with the exact projective test (all n qubits must be correct; zero error tolerance, no loss).
- Required declarationsrequired_declarations
- uniform_bb84_product_state
- single_note_no_oracle
- exact_projective_verifier
- Finite n or asymptoticfinite_n_or_asymptotic
exact for every finite n >= 1
- Parametersparameters
n: number of qubits per note, integer >= 1
- Quantifier over adversariesquantifier_over_adversaries
sup over ALL quantum channels (CPTP maps, unbounded ancilla and computation) from one note to two notes
- Mathematical boundmathematical_bound
P_two_valid(n) = (3/4)^n (tight)
- Numerical methodnumerical_method
log-space: log10 P = n*log10(3/4); float64 then cross-checked in Decimal(60 digits)
- Verification scriptverification_script
qmint/proofs/ideal_bounds.py; tests/unit/proofs/test_ideal_bounds.py
- Independent crosscheckindependent_crosscheck
qmint/proofs/checker.py (Decimal re-derivation); n=1 SDP value 3/4 is lane C (qmint/attacks) deliverable
- Caveatscaveats
- Not a bound for noisy/threshold verifiers (that is game W2), lossy channels, oracle access, or S-money.
- Does not cover the classical-verification variant (P-W1CV) and must not be used for it.
- Statusstatus
PUBLISHED_REPRODUCED
- Boundsbounds
- bound_id: P-W1/unf axis: epsilon_unf anchor: MVW2012 Theorem 1 formula: (3/4)^n domain: n integer >= 1 monotonicity: {}