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. https://resolver.caltech.edu/CaltechAUTHORS:20190212-160252658
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Abstract
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.
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| 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 | |||||||||
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| Subject Keywords: | quantum tomography, projected least squares estimator, low rank states, concentration bounds, optimal estimation | |||||||||
| Issue or Number: | 20 | |||||||||
| DOI: | 10.1088/1751-8121/ab8111 | |||||||||
| Record Number: | CaltechAUTHORS:20190212-160252658 | |||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20190212-160252658 | |||||||||
| 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 | |||||||||
| Collection: | CaltechAUTHORS | |||||||||
| Deposited By: | Bonnie Leung | |||||||||
| Deposited On: | 15 Feb 2019 21:39 | |||||||||
| Last Modified: | 12 Jul 2022 19:52 |
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