Proof obligation · P-S1
KLPR2022 Lemma 1, Eq. (1) (main text p.5; proof SI Note IV)
s_money_kent_2022_ideal_2site · A. Kent, D. Lowndes, D. Pitalua-Garcia, J. Rarity. Practical quantum tokens without quantum memories and experimental tests. npj Quantum Information 8, 28 (2022). doi:10.1038/s41534-022-00524-4
- Status
- PUBLISHED REPRODUCEDLane D reproduced the published bound in code with an independent check.
- Game
- S1
- Anchor
- KLPR2022 Lemma 1, Eq. (1)
- Source file
- proofs/OBLIGATIONS.yaml
Source and theorem
KLPR2022 Lemma 1, Eq. (1) (main text p.5; proof SI Note IV): IQT1 and IQT2 are eps_unf-unforgeable with eps_unf = (1/2 + 1/(2*sqrt(2)))^N.
Citations
Record
Every field of the source record, in file order.
- Protocolprotocol
s_money_kent_2022_ideal_2site
- Gamegame
S1
- Sourcesource
KLPR2022
- Assumptionsassumptions
- Ideal schemes IQT1/IQT2 of Table 1: N exact BB84 qubits with uniformly random states and bases; no loss, no preparation/measurement error, no multiphoton component.
- Exactly two presentation points (M = 1).
- Bob (the bank) follows the scheme honestly; Bob's agents communicate over secure authenticated channels; Alice is arbitrary (unforgeability quantifies over dishonest Alice).
- Required declarationsrequired_declarations
- ideal_no_loss_no_error
- two_presentation_points
- honest_bank_secure_agent_channels
- uniform_bb84_states_and_bases
- Finite n or asymptoticfinite_n_or_asymptotic
exact upper bound for every finite N >= 1
- Parametersparameters
N: number of transmitted qubits, integer >= 1 M: presentation-point pairs; the ideal bound is stated for M = 1 only (optional, default 1)
- Quantifier over adversariesquantifier_over_adversaries
for every (unbounded quantum) strategy of dishonest Alice, P[Bob accepts at both presentation points] <= eps_unf
- Mathematical boundmathematical_bound
(1/2 + 1/(2 sqrt 2))^N
- Numerical methodnumerical_method
log-space
- Verification scriptverification_script
qmint/proofs/ideal_bounds.py
- Independent crosscheckindependent_crosscheck
qmint/proofs/checker.py
- Caveatscaveats
- Not Wiesner's 3/4 bound. Not valid for the realistic schemes QT1/QT2 (use P-S2). No multi-site (M>1) version is stated for the IDEAL schemes; Theorem 2 concerns QT^M only.
- Privacy of IQT is argued in prose only (main text p.4); no numbered privacy lemma for IQT, so the evaluator returns no privacy value for S1.
- Statusstatus
PUBLISHED_REPRODUCED
- Boundsbounds
- bound_id: P-S1/unf axis: epsilon_unf anchor: KLPR2022 Lemma 1, Eq. (1) formula: (1/2 + 1/(2 sqrt 2))^N domain: N integer >= 1, M = 1 monotonicity: {}