Security of two-state and four-state practical quantum bit-commitment protocols
Ricardo Loura, D. Arsenović, Nikola Paunković, Duska B Popovic, Slobodan Prvanović · Physical Review A · 2016
We study cheating strategies against a practical four-state quantum bit-commitment protocol [A. Danan and L. Vaidman, Quant. Info. Proc. 11, 769 (2012)] and its two-state variant [R. Loura et al., Phys. Rev. A 89, 052336 (2014)] when the underlying quantum channels are noisy and the cheating party is constrained to using single-qubit measurements 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 strategy for this bit-commitment protocol. We introduce a strategy, based on certain postmeasurement processes and show it to have better chances at cheating than the direct approach. We also study to what extent sending forged geographical coordinates helps a dishonest party in breaking the binding security requirement. Finally, we investigate the impact of imperfect single-photon sources in the protocols. Our study shows that, in terms of the resources used, the four-state protocol is advantageous over the two-state version. The analysis performed can be straightforwardly generalized to any finite-qubit measurement, with the same qualitative results.