Multipartite Entanglement Certification, with or without Tomography

Yu, N

Multipartite Entanglement Certification, with or without Tomography

Yu, N

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Publisher:: IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
Publication Type:: Journal Article
Citation:: IEEE Transactions on Information Theory, 2020, 66, (10), pp. 6369-6377
Issue Date:: 2020-10-01

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Field	Value	Language
dc.contributor.author	Yu, N https://orcid.org/0000-0003-1188-3032
dc.date.accessioned	2021-03-11T00:47:37Z
dc.date.available	2021-03-11T00:47:37Z
dc.date.issued	2020-10-01
dc.identifier.citation	IEEE Transactions on Information Theory, 2020, 66, (10), pp. 6369-6377
dc.identifier.issn	0018-9448
dc.identifier.issn	1557-9654
dc.identifier.uri	http://hdl.handle.net/10453/147018
dc.description.abstract	© 1963-2012 IEEE. Certifying multipartite entanglement is a fundamental task. Since n-qubit state is parameterized by 4n-1 real numbers, it is interesting to design a measurement setup that detects multipartite entanglement with as little effort as possible, and at a minimum without fully revealing the whole information of the state, the so-called 'tomography'. In this paper, we study the relationship between multipartite entanglement certification and tomography, with the constraint that only single-copy measurements are allowed. We show that by using nonadaptive single-copy measurements, universal entanglement detection, among all states, can not be accomplished without full state tomography. Moreover, we show that almost all multipartite correlations, including the genuine entanglement and the entanglement depth, require full state tomography to detect in this measurement setting. We also observe that universal entanglement detection, among pure states, can be accomplished using much fewer measurements than full state tomography even using only local measurements.
dc.language	English
dc.publisher	IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
dc.relation	http://purl.org/au-research/grants/arc/DE180100156
dc.relation.ispartof	IEEE Transactions on Information Theory
dc.relation.isbasedon	10.1109/TIT.2020.3004566
dc.rights	© 2020 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.	en_US
dc.rights	info:eu-repo/semantics/closedAccess
dc.subject	0801 Artificial Intelligence and Image Processing, 0906 Electrical and Electronic Engineering, 1005 Communications Technologies
dc.subject.classification	Networking & Telecommunications
dc.title	Multipartite Entanglement Certification, with or without Tomography
dc.type	Journal Article
utslib.citation.volume	66
utslib.for	0801 Artificial Intelligence and Image Processing
utslib.for	0906 Electrical and Electronic Engineering
utslib.for	1005 Communications Technologies
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	closed_access	*
pubs.consider-herdc	false
dc.date.updated	2021-03-11T00:47:35Z
pubs.issue	10
pubs.publication-status	Published
pubs.volume	66
utslib.citation.issue	10

Abstract:

© 1963-2012 IEEE. Certifying multipartite entanglement is a fundamental task. Since n-qubit state is parameterized by 4n-1 real numbers, it is interesting to design a measurement setup that detects multipartite entanglement with as little effort as possible, and at a minimum without fully revealing the whole information of the state, the so-called 'tomography'. In this paper, we study the relationship between multipartite entanglement certification and tomography, with the constraint that only single-copy measurements are allowed. We show that by using nonadaptive single-copy measurements, universal entanglement detection, among all states, can not be accomplished without full state tomography. Moreover, we show that almost all multipartite correlations, including the genuine entanglement and the entanglement depth, require full state tomography to detect in this measurement setting. We also observe that universal entanglement detection, among pure states, can be accomplished using much fewer measurements than full state tomography even using only local measurements.

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http://hdl.handle.net/10453/147018