Sample-Optimal Tomography of Quantum States

Haah, J; Harrow, AW; Ji, Z; Wu, X; Yu, N

Sample-Optimal Tomography of Quantum States

Haah, J Harrow, AW Ji, Z

Wu, X Yu, N

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Publication Type:: Journal Article
Citation:: IEEE Transactions on Information Theory, 2017, 63 (9), pp. 5628 - 5641
Issue Date:: 2017-09-01

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Field	Value	Language
dc.contributor.author	Haah, J	en_US
dc.contributor.author	Harrow, AW	en_US
dc.contributor.author	Ji, Z https://orcid.org/0000-0002-7659-3178	en_US
dc.contributor.author	Wu, X	en_US
dc.contributor.author	Yu, N https://orcid.org/0000-0003-1188-3032	en_US
dc.date.issued	2017-09-01	en_US
dc.identifier.citation	IEEE Transactions on Information Theory, 2017, 63 (9), pp. 5628 - 5641	en_US
dc.identifier.issn	0018-9448	en_US
dc.identifier.uri	http://hdl.handle.net/10453/119151
dc.description.abstract	© 1963-2012 IEEE. It is a fundamental problem to decide how many copies of an unknown mixed quantum state are necessary and sufficient to determine the state. Previously, it was known only that estimating states to error \epsilon in trace distance required O(dr^{2}/\epsilon ^{2}) copies for a d -dimensional density matrix of rank r. Here, we give a theoretical measurement scheme (POVM) that requires O (dr/ \delta) \ln ~(d/\delta) copies to estimate \rho to error \delta in infidelity, and a matching lower bound up to logarithmic factors. This implies O((dr / \epsilon ^{2}) \ln ~(d/\epsilon)) copies suffice to achieve error \epsilon in trace distance. We also prove that for independent (product) measurements, \Omega (dr^{2}/\delta ^{2}) / \ln (1/\delta) copies are necessary in order to achieve error \delta in infidelity. For fixed d , our measurement can be implemented on a quantum computer in time polynomial in n.	en_US
dc.relation.ispartof	IEEE Transactions on Information Theory	en_US
dc.relation.isbasedon	10.1109/TIT.2017.2719044	en_US
dc.subject.classification	Networking & Telecommunications	en_US
dc.title	Sample-Optimal Tomography of Quantum States	en_US
dc.type	Journal Article
utslib.citation.volume	9	en_US
utslib.citation.volume	63	en_US
utslib.for	0801 Artificial Intelligence and Image Processing	en_US
utslib.for	0906 Electrical and Electronic Engineering	en_US
utslib.for	1005 Communications Technologies	en_US
pubs.embargo.period	Not known	en_US
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
pubs.issue	9	en_US
pubs.publication-status	Published	en_US
pubs.volume	63	en_US

Abstract:

© 1963-2012 IEEE. It is a fundamental problem to decide how many copies of an unknown mixed quantum state are necessary and sufficient to determine the state. Previously, it was known only that estimating states to error \epsilon in trace distance required O(dr^{2}/\epsilon ^{2}) copies for a d -dimensional density matrix of rank r. Here, we give a theoretical measurement scheme (POVM) that requires O (dr/ \delta) \ln ~(d/\delta) copies to estimate \rho to error \delta in infidelity, and a matching lower bound up to logarithmic factors. This implies O((dr / \epsilon ^{2}) \ln ~(d/\epsilon)) copies suffice to achieve error \epsilon in trace distance. We also prove that for independent (product) measurements, \Omega (dr^{2}/\delta ^{2}) / \ln (1/\delta) copies are necessary in order to achieve error \delta in infidelity. For fixed d , our measurement can be implemented on a quantum computer in time polynomial in n.

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http://hdl.handle.net/10453/119151