Quantum Break

Huan-Yu Ku, Josef Kadlec, Antonín Černoch +8 more

Quantum channels, which break entanglement, incompatibility, or nonlocality, 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 certain temporal quantum correlations, i.e., temporal separability, channel unsteerability, temporal unsteerability, and macrorealism. More specifically, we first define the steerability-breaking channel, which is conceptually similar to the entanglement and nonlocality-breaking channels and prove that it is identical to the incompatibility-breaking channel. Similar to the hierarchy relations of the temporal and spatial quantum correlations, the hierarchy of non-breaking channels is discussed. We then introduce the concept of the channels which break temporal correlations, explain how they are related to the standard breaking channels, and prove the following results: (1) A certain measure of temporal nonseparability can be used to quantify a non-entanglement-breaking channel in the sense that the measure is a memory monotone under the framework of the resource theory of the quantum memory. (2) A non-steerability-breaking channel can be certified with channel steering because the steerability-breaking channel is equivalent to the incompatibility-breaking channel. (3) The temporal steerability and non-macrorealism can, respectively, distinguish the steerability-breaking and the nonlocality-breaking unital channel from their corresponding non-breaking channels. Finally, a two-dimensional depolarizing channel is experimentally implemented as a proof-of-principle example to compare the temporal quantum correlations with non-breaking channels.

Alex Montwill, Ann Breslin

Alex Montwill, Ann Breslin

Huan-Yu Ku, Josef Kadlec, Antonín Černoch +8 more

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.

David W. Kribs, Jeremy Levick, Katrina Olfert +2 more

Abstract Quantum entanglement breaking channels are a fundamental class of quantum operations; originally investigated for quantum information theoretic reasons, their study has since grown to touch on many aspects of quantum information science. Here we investigate the nullspace structures of entanglement breaking channels and we derive a pair of related applications. We show that every operator space of trace zero matrices is the nullspace of an entanglement breaking channel. We derive a test for mixed unitarity of quantum channels based on complementary channel behaviour and entanglement breaking channel nullspaces. We identify conditions that guarantee the existence of private algebras for certain classes of entanglement breaking channels.

Tim Folger