Quantifying Quantumness of Channels Without Entanglement

Huan-Yu Ku; Josef Kadlec; Antonin Cernoch; Marco Tulio Quintino; Wenbin Zhou; Karel Lemr; Neill Lambert; Adam Miranowicz; Shin-Liang Chen; Franco Nori; Yueh-Nan Chen

doi:10.1103/PRXQuantum.3.020338

Quantum Science

Publications: Contribution to journal › Article › Peer Reviewed

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-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 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.

Original language	English
Article number	020338
Number of pages	21
Journal	PRX Quantum
Volume	3
Issue number	2
DOIs	https://doi.org/10.1103/PRXQuantum.3.020338
Publication status	Published - 19 May 2022

Funding

The reported experiment was performed by J.K. under the guidance of A.C.. and K.L. The authors acknowledge Karol Bartkiewicz for his help in numerical postprocessing of our experimental data. This work is supported partially by the National Center for Theoretical Sciences and Ministry of Science and Technology, Taiwan, Grants No. MOST 110-2123-M-006-001 and No. MOST 109-2627-E-006-004, and the Army Research Office (under Grant No. W911NF-19-1-0081). H.Y. acknowledges partial support from the National Center for Theoretical Sciences and Ministry of Science and Technology, Taiwan, Grant No. MOST 110-2811-M-006-546. MTQ acknowledges the Austrian Science Fund (FWF) through the SFB project BeyondC (subproject F7103), a grant from the Foundational Questions Institute (FQXi) as part of the Quantum Information Structure of Spacetime (QISS) Project (qiss.fr). This project has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie Grant Agreement No. 801110 and the Austrian Federal Ministry of Education, Science and Research (BMBWF). It reflects only the authors' view, the EU Agency is not responsible for any use that may be made of the information it contains. N.L. acknowledges partial support from JST PRESTO through Grant No. JPMJPR18GC. A.M. is supported by the Polish National Science Centre (NCN) under the Maestro Grant No. DEC-2019/34/A/ST2/00081. S.-L.C. acknowledges support from the Ministry of Science and Technology Taiwan (Grant No. MOST 110-2811-M-006-539). F.N. is supported in part by Nippon Telegraph and Telephone Corporation (NTT) Research, the Japan Science and Technology Agency (JST) [via the Quantum Leap Flagship Program (Q-LEAP) program, the Moonshot R&D Grant No. JPMJMS2061, the Japan Society for the Promotion of Science (JSPS) [via the Grants-in-Aid for Scientific Research (KAKENHI) Grant No. JP20H00134], the Army Research Office (ARO) (Grant No. W911NF-18-1-0358), the Asian Office of Aerospace Research and Development (AOARD) (via Grant No. FA2386-20-1-4069), and the Foundational Questions Institute Fund (FQXi) via Grant No. FQXi-IAF19-06. J.K. and K.L. acknowledge funding by the Czech Science Foundation (Grant No. 20-17765S) and by Palacky University (IGA_PrF_2021_004).

Austrian Fields of Science 2012

103025 Quantum mechanics
102017 Cryptology

Keywords

CRYPTOGRAPHY
REPEATERS

Access to Document

10.1103/PRXQuantum.3.020338Licence: CC BY 4.0

https://phaidra.univie.ac.at/o:1669401Licence: CC BY 4.0
https://arxiv.org/abs/2106.15784Licence: Other

Cite this

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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-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 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.",

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author = "Huan-Yu Ku and Josef Kadlec and Antonin Cernoch and Quintino, \{Marco Tulio\} and Wenbin Zhou and Karel Lemr and Neill Lambert and Adam Miranowicz and Shin-Liang Chen and Franco Nori and Yueh-Nan Chen",

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AU - Lambert, Neill

AU - Miranowicz, Adam

AU - Chen, Shin-Liang

AU - Nori, Franco

AU - Chen, Yueh-Nan

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Quantifying Quantumness of Channels Without Entanglement

Abstract

Funding

Austrian Fields of Science 2012

Keywords

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Beyond C: Quantum Information Systems Beyond Classical Capabilities

QISS: Quantum Information Structure of Spacetime

Cite this

Quantifying Quantumness of Channels Without Entanglement

Abstract

Funding

Austrian Fields of Science 2012

Keywords

Access to Document

Other files and links

Fingerprint

Projects

Beyond C: Quantum Information Systems Beyond Classical Capabilities

QISS: Quantum Information Structure of Spacetime

Cite this