Ultimate limits for multiple quantum channel discrimination

TL;DR

This paper establishes fundamental limits for discriminating multiple quantum channels, revealing how entanglement enhances performance and providing insights into quantum sensing and communication tasks.

Contribution

It derives a lower bound for the error probability in quantum channel discrimination and shows its achievability under certain symmetries, advancing understanding of quantum hypothesis testing.

Findings

Lower bound for error probability in multi-channel discrimination

Entanglement significantly improves discrimination performance

Application to channel position finding demonstrating practical advantages

Abstract

Quantum hypothesis testing is a central task in the entire field of quantum information theory. Understanding its ultimate limits will give insight into a wide range of quantum protocols and applications, from sensing to communication. Although the limits of hypothesis testing between quantum states have been completely clarified by the pioneering works of Helstrom in the 70s, the more difficult problem of hypothesis testing with quantum channels, i.e., channel discrimination, is less understood. This is mainly due to the complications coming from the use of input entanglement and the possibility of employing adaptive strategies. In this paper, we establish a lower limit for the ultimate error probability affecting the discrimination of an arbitrary number of quantum channels. We also show that this lower bound is achievable when the channels have certain symmetries. As an example, we apply our results to the problem of channel position finding, where the goal is to identify the location of a target channel among multiple background channels. In this general setting, we find that the use of entanglement offers a great advantage over strategies without entanglement, with non-trivial implications for data readout, target detection and quantum spectroscopy.