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arXiv · 1510.02736

Informational completeness in bounded-rank quantum-state tomography

Charles H. Baldwin·Ivan H. Deutsch·Amir Kalev
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Abstract

We consider the problem of quantum-state tomography under the assumption that the state is pure, and more generally that its rank is bounded by a given value. In this scenario, new notions of informationally complete POVMs emerge, which allow for high-fidelity state estimation with fewer measurement outcomes than are required for an arbitrary rank state. We study this in the context of matrix completion, where the POVM outcomes determine only a few of the density matrix elements. We give an analytic solution that fully characterizes informational completeness and elucidates the important role that the positive-semidefinite property of density matrices plays in tomography. We show how positivity can impose a stricter notion of information completeness and allow us to use convex optimization programs to robustly estimate bounded-rank density matrices in the presence of statistical noise.

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Charles H. Baldwin, Ivan H. Deutsch, Amir Kalev. 2016-05-10. Informational completeness in bounded-rank quantum-state tomography. https://doi.org/10.1103/physreva.93.052105

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