Fundamental limits to quantum channel discrimination

TL;DR

This paper establishes fundamental, computable lower bounds on the performance of quantum channel discrimination, revealing ultimate limits and no-go theorems for various quantum information processing tasks.

Contribution

It introduces a new teleportation-based method to simplify adaptive protocols and derives a universal bound based on Choi matrices for quantum channel discrimination.

Findings

Derived a general lower bound for quantum channel discrimination error probability.

Established no-go theorems for quantum illumination and optical resolution.

Applied the methodology to quantum metrology, communication, and secret key generation.

Abstract

What is the ultimate performance for discriminating two arbitrary quantum channels acting on a finite-dimensional Hilbert space? Here we address this basic question by deriving a general and fundamental lower bound. More precisely, we investigate the symmetric discrimination of two arbitrary qudit channels by means of the most general protocols based on adaptive (feedback-assisted) quantum operations. In this general scenario, we first show how port-based teleportation can be used to simplify these adaptive protocols into a much simpler non-adaptive form, designing a new type of teleportation stretching. Then, we prove that the minimum error probability affecting the channel discrimination cannot beat a bound determined by the Choi matrices of the channels, establishing a general, yet computable formula for quantum hypothesis testing. As a consequence of this bound, we derive ultimate limits and no-go theorems for adaptive quantum illumination and single-photon quantum optical resolution. Finally, we show how the methodology can also be applied to other tasks, such as quantum metrology, quantum communication and secret key generation.