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Fast state tomography with optimal error bounds

Guta, M. and Kahn, J. and Kueng, R. and Tropp, J. A. (2020) Fast state tomography with optimal error bounds. Journal of Physics A: Mathematical and General, 53 (20). Art. No. 204001. ISSN 0305-4470. doi:10.1088/1751-8121/ab8111.

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Projected least squares is an intuitive and numerically cheap technique for quantum state tomography: compute the least-squares estimator and project it onto the space of states. The main result of this paper equips this point estimator with rigorous, non-asymptotic convergence guarantees expressed in terms of the trace distance. The estimator's sample complexity is comparable to the strongest convergence guarantees available in the literature and—in the case of the uniform POVM—saturates fundamental lower bounds. Numerical simulations support these competitive features.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
Guta, M.0000-0002-9017-2222
Tropp, J. A.0000-0003-1024-1791
Additional Information:© 2020 IOP Publishing Ltd. Received 31 December 2019; Accepted 18 March 2020; Accepted Manuscript online 18 March 2020; Published 28 April 2020. The authors thank Philippe Faist, Matthias Kleinmann, Anirudh Acharya and Theodore Kypraios for fruitful discussions. Martin Kliesch provided very helpful comments regarding an earlier version of the draft. RK and JT are supported by ONR Award No. N00014-17-12146. RK also acknowledges funding provided by the Institute of Quantum Information and Matter, an NSF Physics Frontiers Center (NSF Grant PHY-1733907).
Group:Institute for Quantum Information and Matter
Funding AgencyGrant Number
Office of Naval Research (ONR)N00014-17-12146
Institute for Quantum Information and Matter (IQIM)UNSPECIFIED
Subject Keywords:quantum tomography, projected least squares estimator, low rank states, concentration bounds, optimal estimation
Issue or Number:20
Record Number:CaltechAUTHORS:20190212-160252658
Persistent URL:
Official Citation:M Guţă et al 2020 J. Phys. A: Math. Theor. 53 204001
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:92858
Deposited By: Bonnie Leung
Deposited On:15 Feb 2019 21:39
Last Modified:12 Jul 2022 19:52

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