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Fast state tomography with optimal error bounds. (arXiv:1809.11162v1 [quant-ph])
来源于:arXiv
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. 查看全文>>