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Fast state tomography with optimal error bounds

Guta, Madalin and Kahn, Jonas and Kueng, Richard and Tropp, Joel A. (2018) Fast state tomography with optimal error bounds. . (Submitted)

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Projected least squares (PLS) is an intuitive and numerically cheap technique for quantum state tomography. The method first computes the least-squares estimator (or a linear inversion estimator) and then projects the initial estimate onto the space of states. The main result of this paper equips this point estimator with a rigorous, non-asymptotic confidence region expressed in terms of the trace distance. The analysis holds for a variety of measurements, including 2-designs and Pauli measurements. The sample complexity of the estimator is comparable to the strongest convergence guarantees available in the literature and---in the case of measuring the uniform POVM---saturates fundamental lower bounds.The results are derived by reinterpreting the least-squares estimator as a sum of random matrices and applying a matrix-valued concentration inequality. The theory is supported by numerical simulations for mutually unbiased bases, Pauli observables, and Pauli basis measurements.

Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription Paper
Tropp, Joel A.0000-0003-1024-1791
Additional Information:The authors thank Philippe Faist, Anirudh Acharya and Theodore Kypraios for fruitful discussions and valuable feedback. 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:IQIM, 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
Record Number:CaltechAUTHORS:20190212-160252658
Persistent URL:
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:03 Oct 2019 20:49

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