Strictly-complete measurements for bounded-rank quantum-state tomography
arXiv:1605.02109 · doi:10.1103/PhysRevA.93.052105
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 two notions of informationally complete measurements emerge: rank- complete measurements and rank- strictly-complete measurements. Whereas in the first notion, a rank- state is uniquely identified from within the set of rank- states, in the second notion the same state is uniquely identified from within the set of all physical states, of any rank. We argue, therefore, that strictly-complete measurements are compatible with convex optimization, and we prove that they allow robust quantum state estimation in the presence of experimental noise. We also show that rank- strictly-complete measurements are as efficient as rank- complete measurements. We construct examples of strictly-complete measurements and give a complete description of their structure in the context of matrix completion. Moreover, we numerically show that a few random bases form such measurements. We demonstrate the efficiency-robustness property for different strictly-complete measurements with numerical experiments. We thus conclude that only strictly-complete measurements are useful for practical tomography.
arXiv commentThis is a combined version of arXiv:1510.02736 and arXiv:1511.01433
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