Multi-state and multi-hypothesis discrimination with open quantum systems. (arXiv:1802.02849v1 [quant-ph])

We show how an upper bound for the ability to discriminate any number N of
candidates for the Hamiltonian governing the evolution of an open quantum
system may be calculated by numerically efficient means. Our method applies an
effective master equation analysis to evaluate the pairwise overlaps between
candidate full states of the system and its environment pertaining to the
Hamiltonians. These overlaps are then used to construct an N -dimensional
representation of the states. The optimal positive-operator valued measure
(POVM) and the corresponding probability of assigning a false hypothesis may
subsequently be evaluated by phrasing optimal discrimination of multiple
non-orthogonal quantum states as a semi-definite programming problem. We
investigate the structure of the optimal POVM and we provide three realistic
examples of hypothesis testing with open quantum systems.

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