Proof obligation · P-W1CV
MVW2012 Theorem 2 (p.3)
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_CV
- Anchor
- MVW2012 Theorem 2
- Source file
- proofs/OBLIGATIONS.yaml
Source and theorem
MVW2012 Theorem 2 (p.3): for the classical-verification analogue of Wiesner's scheme, the optimal simple counterfeiting attack succeeds in two independent verifications with probability exactly (3/4 + sqrt(2)/8)^n.
Citations
Record
Every field of the source record, in file order.
- Protocolprotocol
wiesner_ideal
- Gamegame
W1_CV
- Sourcesource
MVW2012
- Assumptionsassumptions
- Note as in P-W1; verification = bank sends a uniformly random challenge c in {0,1}^n, holder returns measurement outcomes, bank checks positions where c matches the preparation basis.
- Adversary holds ONE valid note and tries to pass TWO independent classical verifications.
- Exact acceptance rule (no error tolerance, no loss), no other oracle access.
- Required declarationsrequired_declarations
- uniform_bb84_product_state
- single_note_no_oracle
- uniform_classical_challenge
- exact_classical_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 strategies holding one note and answering two independent challenges
- Mathematical boundmathematical_bound
(3/4 + sqrt(2)/8)^n (tight)
- Numerical methodnumerical_method
log-space as P-W1
- Verification scriptverification_script
qmint/proofs/ideal_bounds.py; tests/unit/proofs/test_ideal_bounds.py
- Independent crosscheckindependent_crosscheck
qmint/proofs/checker.py
- Caveatscaveats
- A different game from W1; its base 0.9268 is LARGER than 3/4 - substituting (3/4)^n here would be optimistic.
- Statusstatus
PUBLISHED_REPRODUCED
- Boundsbounds
- bound_id: P-W1CV/unf axis: epsilon_unf anchor: MVW2012 Theorem 2 formula: (3/4 + sqrt(2)/8)^n domain: n integer >= 1 monotonicity: {}