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arXiv · 1809.11162

Fast state tomography with optimal error bounds

Madalin Guta·Jonas Kahn·Richard Kueng·Joel A. Tropp
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Abstract

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.

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Madalin Guta, Jonas Kahn, Richard Kueng, Joel A. Tropp. 2018-09-28. Fast state tomography with optimal error bounds. https://arxiv.org/abs/1809.11162

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