Secret parameters in quantum bit commitment

TL;DR

This paper revises the no-go theorem for quantum bit commitment by showing that the assumption of Alice knowing Bob's secret parameters is unnecessary, thus refining the understanding of the protocol's security limitations.

Contribution

It demonstrates that the cheating transformation in quantum bit commitment is independent of Bob's secret parameters, challenging a key assumption in the original no-go theorem.

Findings

The cheating unitary transformation is independent of Bob's secret choices.

The original impossibility proof was based on an incorrect assumption.

The result closes a loophole in the no-go theorem.

Abstract

The no-go theorem of unconditionally secure quantum bit commitment depends crucially on the assumption that Alice knows in detail all the probability distributions generated by Bob. We show that if a protocol is concealing, then the cheating unitary transformation is independent of any parameters (including probability distributions) secretly chosen by Bob, so that Alice can calculate it without knowing Bob's secret choices. Otherwise the protocol cannot be concealing. Our result shows that the original impossibility proof was based on an incorrect assumption, despite the fact that its conclusion remains valid within the adopted framework. Furthermore, our result eliminates a potential loophole in the no-go theorem.