Fast state tomography with optimal error bounds. (28th April 2020)

• Record Type: Journal Article
• Authors: Guţă, M; Kahn, J; Kueng, R; Tropp, J A
• Is Part Of: Journal of physics. Volume 53:Number 20(2020)
• Publication Date: 2020-04-28
• Subjects: quantum tomography -- projected least squares estimator -- low rank states -- concentration bounds -- optimal estimation; Mathematical physics -- Periodicals; Statistical physics -- Periodicals; Quantum theory -- Periodicals; Matter -- Properties -- Periodicals; 530.105
• DOI: 10.1088/1751-8121/ab8111
• Languages: English
• ISSNs: 1751-8113

Abstract

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.