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Quantum State Tomography via Compressed Sensing

Gross, David and Liu, Yi-Kai and Flammia, Steven T. and Becker, Stephen and Eisert, Jens (2010) Quantum State Tomography via Compressed Sensing. Physical Review Letters, 105 (15). Art. No. 150401. ISSN 0031-9007. https://resolver.caltech.edu/CaltechAUTHORS:20101025-113049538

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Abstract

We establish methods for quantum state tomography based on compressed sensing. These methods are specialized for quantum states that are fairly pure, and they offer a significant performance improvement on large quantum systems. In particular, they are able to reconstruct an unknown density matrix of dimension d and rank r using O(rdlog^2d) measurement settings, compared to standard methods that require d^2 settings. Our methods have several features that make them amenable to experimental implementation: they require only simple Pauli measurements, use fast convex optimization, are stable against noise, and can be applied to states that are only approximately low rank. The acquired data can be used to certify that the state is indeed close to pure, so no a priori assumptions are needed.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1103/PhysRevLett.105.150401 DOIArticle
http://prl.aps.org/abstract/PRL/v105/i15/e150401PublisherArticle
ORCID:
AuthorORCID
Gross, David0000-0001-8888-3028
Additional Information:© 2010 The American Physical Society. Received 21 October 2009; published 4 October 2010. We thank E. Candès and Y. Plan for useful discussions. Research at PI is supported by the Government of Canada through Industry Canada and by the Province of Ontario through the Ministry of Research & Innovation. Y. L. is supported by the NSF, J. E. by the EU (QAP, QESSENCE, MINOS, COMPAS) and the EURYI, D. G. by the EU (CORNER). We thank the anonymous referees for many helpful suggestions.
Funders:
Funding AgencyGrant Number
Industry CanadaUNSPECIFIED
Ontario Ministry of Research InnovationUNSPECIFIED
NSFUNSPECIFIED
European Union (EU)UNSPECIFIED
European Young Investigator Awards (EURYI)UNSPECIFIED
Issue or Number:15
Classification Code:PACS: 03.65.Wj, 03.67.-a
Record Number:CaltechAUTHORS:20101025-113049538
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20101025-113049538
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:20506
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:15 Nov 2010 19:41
Last Modified:09 Mar 2020 13:18

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