Fundamental limits to quantum channel discrimination

Stefano Pirandola,Riccardo Laurenza,Jason L. Pereira,Cosmo Lupo

doi:10.1038/s41534-019-0162-y

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.

Highlights

Quantum hypothesis testing[1] is a central area in quantum information theory,[2,3] with many studies for both discrete variable (DV)[4] and continuous variable (CV) systems.[5]
Let us formulate the most general adaptive protocol over an arbitrary quantum channel E defined between Hilbert spaces of dimension d
The registers will be in a state ρn which depends on E and the sequence of quantum operations (QOs) {Λ0, Λ1, ..., Λn} defining the adaptive protocol Pn with output state ρn

Summary

Introduction

Quantum hypothesis testing[1] is a central area in quantum information theory,[2,3] with many studies for both discrete variable (DV)[4] and continuous variable (CV) systems.[5]. 19 presented two channels which can be perfectly distinguished by using feedback in just two adaptive uses, while they cannot be perfectly discriminated by any number of uses of a block (non-adaptive) protocol, where the channels are probed in an identical and independent fashion. This suggests that the best discrimination performance is not directly related to the diamond distance,[20] when computed over multiple copies of the quantum channels. In this work we fill this fundamental gap by deriving a universal computable lower bound for the error probability affecting the discrimination of two arbitrary quantum channels

Methods

Results

Conclusion