Bounds on amplitude damping channel discrimination

TL;DR

This paper derives tighter bounds on the distinguishability of amplitude damping channels, accounting for adaptive strategies, with implications for quantum sensing and security.

Contribution

It introduces new analytical bounds on the diamond norm for AD channels and improves existing bounds on discrimination error probabilities.

Findings

Analytical expression for the diamond norm between AD channels.

Tighter upper bounds on the trace norm for adaptive discrimination protocols.

Application of bounds to quantum hacking and biological sensing scenarios.

Abstract

Amplitude damping (AD) channels are good models for many physical scenarios, and so the development of protocols to discriminate between them is an important task in quantum information science. It is therefore important to bound the performance of such protocols. Since adaptivity has been shown to improve the performance of discrimination protocols, bounds on the distinguishability of AD channels must take this into account. In this paper, we use both channel simulation and a bound based on the diamond norm to significantly tighten the upper bound on the trace norm between the possible outputs of binary channel discrimination protocols acting on AD channels (and hence the lower bound on the error probability of such protocols). The diamond norm between any two AD channels is found analytically, giving the optimal error probability for a one-shot discrimination protocol. We also present a tighter lower bound on the achievable trace norm between protocol outputs (and a corresponding upper bound on the achievable error probability). The upper and lower bounds are compared with existing bounds and then applied to quantum hacking and biological quantum sensing scenarios.