Disguising quantum channels by mixing and channel distance trade-off

TL;DR

This paper introduces the disguising problem for quantum channels, exploring how to make two channels identical through minimal mixing and analyzing the trade-offs involved, with implications for quantum cryptography.

Contribution

It formulates the disguising problem, derives bounds on the mixing trade-off, and relates it to channel distinguishability and cryptographic key rates.

Findings

Derived bounds on the trade-off curve for channel disguising

Established the relationship between disguising and distinguishability

Applied bounds to example channels and obtained optimal trade-off in one case

Abstract

We consider the reverse problem to the distinguishability of two quantum channels, which we call the disguising problem. Given two quantum channels, the goal here is to make the two channels identical by mixing with some other channels with minimal mixing probabilities. This quantifies how much one channel can disguise as the other. In addition, the possibility to trade off between the two mixing probabilities allows one channel to be more preserved (less mixed) at the expense of the other. We derive lower- and upper-bounds of the trade-off curve and apply them to a few example channels. Optimal trade-off is obtained in one example. We relate the disguising problem and the distinguishability problem by showing the the former can lower and upper bound the diamond norm. We also show that the disguising problem gives an upper bound on the key generation rate in quantum cryptography.