Quantum State Tomography via Compressed Sensing
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.
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.Attached Files
Published - Gross2010p11625Phys_Rev_Lett.pdf
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Additional details
- Eprint ID
- 20506
- Resolver ID
- CaltechAUTHORS:20101025-113049538
- Industry Canada
- Ontario Ministry of Research Innovation
- NSF
- European Union (EU)
- European Young Investigator Awards (EURYI)
- Created
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2010-11-15Created from EPrint's datestamp field
- Updated
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2021-11-09Created from EPrint's last_modified field