Quantifying Quantumness of Channels Without Entanglement

TL;DR

This paper explores the relationship between quantum channels that do not break entanglement or nonlocality and macrorealism tests, introducing new measures and hierarchies for non-breaking channels, supported by an experimental demonstration.

Contribution

It introduces the concept of steerability-breaking channels, proves their equivalence to incompatibility-breaking channels, and establishes a hierarchy of non-breaking channels with experimental validation.

Findings

Steerability-breaking channels are equivalent to incompatibility-breaking channels.

A hierarchy of non-breaking channels is established based on temporal and spatial correlations.

Experimental implementation of a depolarizing channel demonstrates the hierarchy of non-breaking channels.

Abstract

Quantum channels breaking entanglement, incompatibility, or nonlocality are defined as such because they are not useful for entanglement-based, one-sided device-independent, or device-independent quantum information processing, respectively. Here, we show that such breaking channels are related to complementary tests of macrorealism i.e., temporal separability, channel unsteerability, temporal unsteerability, and the temporal Bell inequality. To demonstrate this we first define a steerability-breaking channel, which is conceptually similar to entanglement and nonlocality-breaking channels and prove that it is identical to an incompatibility-breaking channel. A hierarchy of quantum non-breaking channels is derived, akin to the existing hierarchy relations for temporal and spatial quantum correlations. We then introduce the concept of channels that break temporal correlations, explain how they are related to the standard breaking channels, and prove the following results: (1) A robustness-based measure for non-entanglement-breaking channels can be probed by temporal nonseparability. (2) A non-steerability-breaking channel can be quantified by channel steering. (3) Temporal steerability and non-macrorealism can be used for, respectively, distinguishing unital steerability-breaking channels and nonlocality-breaking channels for a maximally entangled state. Finally, a two-dimensional depolarizing channel is experimentally implemented as a proof-of-principle example to demonstrate the hierarchy relation of non-breaking channels using temporal quantum correlations