# On the question of secret probability distributions in quantum bit commitment

## TL;DR

This paper explores how secret probability distributions used by Bob in quantum bit commitment affect the security proof, showing that secret distributions lead to mixed states and impact Alice's ability to cheat.

## Contribution

It provides a simplified proof that secret distributions by Bob influence the no-go theorem, extending the analysis to imperfect concealing scenarios.

## Key findings

- Secret distributions lead to mixed quantum states.
- Alice's cheating ability remains possible with secret distributions.
- The proof extends to imperfect concealing cases.

## Abstract

The proof of the No-Go Theorem of unconditionally secure quantum bit commitment depends on the assumption that Alice knows every detail of the protocol, including the probability distributions associated with all the random variables generated by Bob. We argue that this condition may not be universally satisfied. In fact it can be shown that when Bob is allowed to use a secret probability distribution, the joint quantum state is inevitably mixed. It is then natural to ask if Alice can still cheat. A positive answer has been given by us [13] for the perfect concealing case. In this paper, we present a simplified proof of our previous result, and extend it to cover the imperfect concealing case as well.