Fast state tomography with optimal error bounds

Guta, M; Kahn, J; Kueng, R; Tropp, J A

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.

Citation

Guta, M., Kahn, J., Kueng, R., & Tropp, J. A. (2020). Fast state tomography with optimal error bounds. Journal of Physics A: Mathematical and Theoretical, 53(20), https://doi.org/10.1088/1751-8121/ab8111

• Journal Article Type: Article
• Acceptance Date: Mar 18, 2020
• Online Publication Date: Apr 28, 2020
• Publication Date: 2020-05
• Deposit Date: Oct 16, 2020
• Publicly Available Date: Oct 16, 2020
• Journal: Journal of Physics A: Mathematical and Theoretical
• Print ISSN: 1751-8113
• Electronic ISSN: 1751-8121
• Publisher: IOP Publishing
• Peer Reviewed: Peer Reviewed
• Volume: 53
• Issue: 20
• Article Number: 204001
• DOI: https://doi.org/10.1088/1751-8121/ab8111
• Keywords: Modelling and Simulation; Statistics and Probability; Mathematical Physics; General Physics and Astronomy; Statistical and Nonlinear Physics
• Public URL: https://nottingham-repository.worktribe.com/output/4176274
• Publisher URL: https://iopscience.iop.org/article/10.1088/1751-8121/ab8111