Optimal environment localization

TL;DR

This paper investigates quantum channel position finding in bosonic systems, deriving bounds and protocols that often outperform classical strategies, with applications in thermal imaging and noise localization.

Contribution

It introduces a quantum advantage condition and explicit protocols for channel position finding, advancing quantum hypothesis testing methods.

Findings

Derived bounds for multi-ary quantum channel discrimination

Established conditions for quantum advantage over classical protocols

Designed explicit protocols achieving often optimal error probabilities

Abstract

Quantum channels model many physical processes. For this reason, hypothesis testing between quantum channels is a fundamental task in quantum information theory. Here we consider the paradigmatic case of channel position finding, where the aim is to determine the position of a target quantum channel within a sequence of background channels. We explore this model in the setting of bosonic systems, considering Gaussian channels with the same transmissivity (or gain) but different levels of environmental noise. Thus the goal of the problem becomes detecting the position of a target environment among a number of identical background environments, all acting on an input multi-mode system. We derive bounds for the ultimate error probability affecting this multi-ary discrimination problem and find an analytic condition for quantum advantage over protocols involving classical input states. We also design an explicit protocol that gives numerical bounds on the ultimate error probability and often achieves quantum advantage. Finally, we consider direct applications of the model for tasks of thermal imaging (finding a warmer pixel in a colder background) and quantum communication (for localizing a different level of noise in a sequence of lines or a frequency spectrum).