Sample efficient identity testing and independence testing of quantum states

Yu, N

Sample efficient identity testing and independence testing of quantum states

Yu, N

Permalink

Publication Type:: Conference Proceeding
Citation:: Leibniz International Proceedings in Informatics, LIPIcs, 2021, 185
Issue Date:: 2021-02-01

Open Access

Copyright Clearance Process

Recently Added
In Progress
Open Access

This item is open access.

Adobe PDF

Download Published versionAdobe PDF (626.78 kB)

View on publisher's site

View statistics

Full metadata record

Field	Value	Language
dc.contributor.author	Yu, N https://orcid.org/0000-0003-1188-3032
dc.date.accessioned	2022-03-31T03:56:00Z
dc.date.available	2022-03-31T03:56:00Z
dc.date.issued	2021-02-01
dc.identifier.citation	Leibniz International Proceedings in Informatics, LIPIcs, 2021, 185
dc.identifier.isbn	9783959771771
dc.identifier.issn	1868-8969
dc.identifier.uri	http://hdl.handle.net/10453/155763
dc.description.abstract	In this paper, we study the quantum identity testing problem, i.e., testing whether two given quantum states are identical, and quantum independence testing problem, i.e., testing whether a given multipartite quantum state is in tensor product form. For the quantum identity testing problem of D(Cd) system, we provide a deterministic measurement scheme that uses O(dε22) copies via independent measurements with d being the dimension of the state and ε being the additive error. For the independence testing problem D(Cd1 ⊗ Cd2 ⊗ · · · ⊗ Cdm) system, we show that the sample complexity is Θ(~ Πmi=1ε2di) via collective measurements, and O(Πmi=1ε2d2i) via independent measurements. If randomized choice of independent measurements are allowed, the sample complexity is Θ(d3ε2/2) for the quantum identity testing problem, and Θ(~ Πmi=1ε2d3 i/2) for the quantum independence testing problem.
dc.language	en
dc.relation.ispartof	Leibniz International Proceedings in Informatics, LIPIcs
dc.relation.isbasedon	10.4230/LIPIcs.ITCS.2021.11
dc.rights	info:eu-repo/semantics/openAccess
dc.title	Sample efficient identity testing and independence testing of quantum states
dc.type	Conference Proceeding
utslib.citation.volume	185
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	*
dc.date.updated	2022-03-31T03:55:59Z
pubs.publication-status	Published
pubs.volume	185

Abstract:

In this paper, we study the quantum identity testing problem, i.e., testing whether two given quantum states are identical, and quantum independence testing problem, i.e., testing whether a given multipartite quantum state is in tensor product form. For the quantum identity testing problem of D(Cd) system, we provide a deterministic measurement scheme that uses O(dε22) copies via independent measurements with d being the dimension of the state and ε being the additive error. For the independence testing problem D(Cd1 ⊗ Cd2 ⊗ · · · ⊗ Cdm) system, we show that the sample complexity is Θ(~ Πmi=1ε2di) via collective measurements, and O(Πmi=1ε2d2i) via independent measurements. If randomized choice of independent measurements are allowed, the sample complexity is Θ(d3ε2/2) for the quantum identity testing problem, and Θ(~ Πmi=1ε2d3 i/2) for the quantum independence testing problem.

Please use this identifier to cite or link to this item:

http://hdl.handle.net/10453/155763