Secure quantum bit commitment against empty promises. II. The density matrix

TL;DR

This paper analyzes the security of a specific quantum bit commitment protocol by examining the reduced density matrices, showing it can be concealing while remaining secure against certain cheating strategies, thus challenging existing no-go theorems.

Contribution

It demonstrates that the protocol's security relies on the orthogonality of reduced density matrices, providing a counterexample to the assumptions of the no-go theorem.

Findings

The reduced density matrices ^B and ^B are orthogonal.

The protocol remains concealing to Bob.

The no-go theorem's assumptions do not apply to this protocol.

Abstract

We further study the security of the quantum bit commitment (QBC) protocol we previously proposed [Phys. Rev. A 74, 022332 (2006).], by analyzing the reduced density matrix \rho_{b}^{B} which describes the quantum state at Bob's side corresponding to Alice's committed bit b. It is shown that Alice will find \rho_{0}^{B}\perp \rho_{1}^{B} while the protocol remains concealing to Bob. On the contrary, the existing no-go theorem of unconditionally secure QBC is based on the condition \rho_{0}^{B}\simeq \rho_{1}^{B}. Thus the specific cheating strategy proposed in the no-go theorem does not necessarily applies to our protocol.