Process output nonclassicality and nonclassicality depth of quantum-optical channels

TL;DR

This paper introduces a new framework for quantifying the nonclassicality of quantum-optical channels based on their output states, including a measure called nonclassicality depth that indicates the noise level needed to make a channel classical.

Contribution

It proposes a stronger nonclassicality criterion for quantum channels, compares it with previous approaches, and extends the nonclassicality depth measure to multimode quantum channels.

Findings

The new nonclassicality criterion is stronger than previous ones.

A noise-robustness measure called nonclassicality depth is introduced.

The framework is extended to multimode quantum channels.

Abstract

We introduce a quantum-optical notion of nonclassicality that we call as the process output nonclassicality for multimode quantum channels. The motivation comes from an information-theoretic point of view and the emphasis is on the output states of a channel. We deem a channel to be `classical' if its outputs are always classical irrespective of the input, i.e., if the channel is nonclassicality breaking, and nonclassical otherwise. Our condition is stronger than the one considered by Rahimi-Keshari et al. [PRL {\bf 110}, 160401 (2013)] and we compare the two approaches. Using our framework we then quantify the nonclassicality of a quantum process by introducing a noise-robustness type of measure that we call as the nonclassicality depth of a channel. It characterizes a certain threshold noise beyond which a given channel outputs only classical states. We achieve this by generalizing a prescription by Lee [PRA {\bf 44}, R2775 (1991)] to multimode states and then by extension to multimode channels.