Unambiguous discrimination of the change point for quantum channels

TL;DR

This paper explores the fundamental limits of unambiguous quantum channel change point detection, providing bounds and analytical expressions for success probabilities in quantum process discrimination.

Contribution

It introduces a method to derive bounds on success probability for unambiguous change point detection in quantum channels, especially for unitary channels.

Findings

Derived bounds on maximum success probability for change point detection.

Provided analytical expressions for success probability with unitary channels.

Highlighted the challenge of analytical solutions in quantum process discrimination.

Abstract

Identifying the precise moment when a quantum channel undergoes a change is a fundamental problem in quantum information theory. We study how accurately one can determine the time at which a channel transitions to another. We investigate the quantum limit of the average success probability in unambiguous discrimination, in which errors are completely avoided by allowing inconclusive results with a certain probability. This problem can be viewed as a quantum process discrimination task, where the process consists of a sequence of quantum channels; however, obtaining analytical solutions for quantum process discrimination is generally extremely challenging. In this paper, we propose a method to derive lower and upper bounds on the maximum average success probability in unambiguous discrimination. In particular, when the channels before and after the change are unitary, we show that the maximum average success probability can be analytically expressed in terms of the length of the channel sequence and the discrimination limits for the two channels.