arXiv:2106.15784 · PRX Quantum

Quantifying Quantumness of Channels Without Entanglement

Huan-Yu Ku, Josef Kadlec, Antonín Černoch, Marco Túlio Quintino, Wenbin Zhou, Karel Lemr, Neill Lambert, Adam Miranowicz, Shin-Liang Chen, Franco Nori, Yueh-Nan Chen

Published May 19, 2022• 42 citations

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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 nonbreaking 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-entanglementbreaking channels can be probed by temporal nonseparability.(2) A non-steerability-breaking channel can be quantified by channel steering.(3) Temporal steerability and nonmacrorealism 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 nonbreaking channels using temporal quantum correlations.

DOI: 10.1103/prxquantum.3.020338

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