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Fast state tomography with optimal error bounds
Journal of Physics A: Mathematical and Theoretical ( IF 2.1 ) Pub Date : 2020-04-29 , DOI: 10.1088/1751-8121/ab8111
M Guţă 1 , J Kahn 2 , R Kueng 3 , J A Tropp 3
Affiliation  

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.

中文翻译:

具有最佳误差范围的快速状态层析成像

投影最小二乘法是一种用于量子态层析成像的直观且价格便宜的技术:计算最小二乘估计器并将其投影到状态空间上。本文的主要结果为该点估计器提供了严格的,非渐近收敛保证,以迹距表示。估计器的样本复杂度可与文献中提供的最强收敛保证相媲美,并且在统一POVM的情况下,会使基本下限达到饱和。数值模拟支持了这些竞争特征。
更新日期:2020-04-29
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