Quantum earth mover's distance, a no-go quantum Kantorovich-Rubinstein theorem, and quantum marginal problem

Zhou, L; Yu, N; Ying, S; Ying, M

Quantum earth mover's distance, a no-go quantum Kantorovich-Rubinstein theorem, and quantum marginal problem

Zhou, L Yu, N

Ying, S Ying, M

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Publisher:: AIP Publishing
Publication Type:: Journal Article
Citation:: Journal of Mathematical Physics, 2022, 63, (10)
Issue Date:: 2022-10-01

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Field	Value	Language
dc.contributor.author	Zhou, L
dc.contributor.author	Yu, N https://orcid.org/0000-0003-1188-3032
dc.contributor.author	Ying, S
dc.contributor.author	Ying, M https://orcid.org/0000-0003-4847-702X
dc.date.accessioned	2023-03-20T23:07:02Z
dc.date.available	2023-03-20T23:07:02Z
dc.date.issued	2022-10-01
dc.identifier.citation	Journal of Mathematical Physics, 2022, 63, (10)
dc.identifier.issn	0022-2488
dc.identifier.issn	1089-7658
dc.identifier.uri	http://hdl.handle.net/10453/167822
dc.description.abstract	The quantum coupling of two given quantum states denotes the set of bipartite states whose marginal states are these given two states. In this paper, we provide tight inequalities to describe the structure of quantum coupling. These inequalities directly imply that the trace distance between two quantum states cannot be determined by the quantum analog of the earth mover's distance, thus ruling out the equality version of the quantum Kantorovich-Rubinstein theorem for trace distance even in the finite-dimensional case. In addition, we provide an inequality that can be regarded as a quantum generalization of the Kantorovich-Rubinstein theorem. Then, we generalize our inequalities and apply them to the three tripartite quantum marginal problems. Numerical tests with a three-qubit system show that our criteria are much stronger than the known criteria: the strong subadditivity of entropy and the monogamy of entanglement.
dc.language	English
dc.publisher	AIP Publishing
dc.relation	http://purl.org/au-research/grants/arc/DE180100156
dc.relation	http://purl.org/au-research/grants/arc/DP210102449
dc.relation.ispartof	Journal of Mathematical Physics
dc.relation.isbasedon	10.1063/5.0068344
dc.rights	info:eu-repo/semantics/embargoedAccess
dc.subject	01 Mathematical Sciences, 02 Physical Sciences
dc.subject.classification	Mathematical Physics
dc.title	Quantum earth mover's distance, a no-go quantum Kantorovich-Rubinstein theorem, and quantum marginal problem
dc.type	Journal Article
utslib.citation.volume	63
utslib.for	01 Mathematical Sciences
utslib.for	02 Physical Sciences
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology
pubs.organisational-group	/University of Technology Sydney/Strength - QSI - Centre for Quantum Software and Information
utslib.copyright.status	open_access	*
utslib.copyright.embargo	2023-10-01T00:00:00+1000Z
dc.date.updated	2023-03-20T23:07:01Z
pubs.issue	10
pubs.publication-status	Published
pubs.volume	63
utslib.citation.issue	10

Abstract:

The quantum coupling of two given quantum states denotes the set of bipartite states whose marginal states are these given two states. In this paper, we provide tight inequalities to describe the structure of quantum coupling. These inequalities directly imply that the trace distance between two quantum states cannot be determined by the quantum analog of the earth mover's distance, thus ruling out the equality version of the quantum Kantorovich-Rubinstein theorem for trace distance even in the finite-dimensional case. In addition, we provide an inequality that can be regarded as a quantum generalization of the Kantorovich-Rubinstein theorem. Then, we generalize our inequalities and apply them to the three tripartite quantum marginal problems. Numerical tests with a three-qubit system show that our criteria are much stronger than the known criteria: the strong subadditivity of entropy and the monogamy of entanglement.

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http://hdl.handle.net/10453/167822