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We study cheating strategies against a practical four-state quantumbit-commitment protocol and its two-state variant when the underlying quantumchannels are noisy and the cheating party is constrained to using single-qubitmeasurements only. We show that simply inferring the transmitted photons'states by using the Breidbart basis, optimal for ambiguous (minimum-error)state discrimination, does not directly produce an optimal cheating strategyfor this bit-commitment protocol. We introduce a new strategy, based on certainpost-measurement processes, and show it to have better chances at cheating thanthe direct approach. We also study to what extent sending forged geographicalcoordinates helps a dishonest party in breaking the binding securityrequirement. Finally, we investigate the impact of imperfect single-photonsources in the protocols. Our study shows that, in terms of the resources used,the four-state protocol is advantageous over the two-state version. Theanalysis performed can be straightforwardly generalised to any finite-qubitmeasurement, with the same qualitative results.

Security of two-state and four-state practical quantum bit-commitment protocols