Quantum advantage for noisy channel discrimination

TL;DR

This paper demonstrates that quantum advantage in channel discrimination persists even with noisy processes, revealing a transition between coherent and incoherent strategies influenced by noise levels.

Contribution

It introduces a hybrid protocol that maintains quantum advantage under noise and provides a framework based on quantum signal processing for realistic noisy scenarios.

Findings

Quantum advantage persists with noisy channels.

Transition between coherent and incoherent strategies depends on noise.

Hybrid strategies outperform purely incoherent protocols in intermediate noise regimes.

Abstract

Many quantum mechanical experiments can be viewed as multi-round interactive protocols between known quantum circuits and an unknown quantum process. Fully quantum "coherent" access to the unknown process is known to provide an advantage in many discrimination tasks compared to when only incoherent access is permitted, but it is unclear if this advantage persists when the process is noisy. Here, we show that a quantum advantage can be maintained when distinguishing between two noisy single qubit rotation channels. Numerical and analytical calculations reveal a distinct transition between optimal performance by fully coherent and fully incoherent protocols as a function of noise strength. Moreover, the size of the region of coherent quantum advantage shrinks inverse polynomially in the number of channel uses, and in an intermediate regime an improved strategy is a hybrid of fully-coherent and fully-incoherent subroutines. The fully coherent protocol is based on quantum signal processing, suggesting a generalizable algorithmic framework for the study of quantum advantage in the presence of realistic noise.