Generalized quantum state discrimination problems
arXiv:1501.05744 · doi:10.1103/PhysRevA.91.052304
Abstract
We address a broad class of optimization problems of finding quantum measurements, which includes the problems of finding an optimal measurement in the Bayes criterion and a measurement maximizing the average success probability with a fixed rate of inconclusive results. Our approach can deal with any problem in which each of the objective and constraint functions is formulated by the sum of the traces of the multiplication of a Hermitian operator and a detection operator. We first derive dual problems and necessary and sufficient conditions for an optimal measurement. We also consider the minimax version of these problems and provide necessary and sufficient conditions for a minimax solution. Finally, for optimization problem having a certain symmetry, there exists an optimal solution with the same symmetry. Examples are shown to illustrate how our results can be used.
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- Ultimate limits of approximate unambiguous discrimination
- Quasi-Bell entangled coherent states and its quantum discrimination problem in the presence of thermal noise
- Quantum enhancement of spoofing detection with squeezed states of light
- Upper and Lower Bounds on Optimal Success Probability of Quantum State Discrimination with and without Inconclusive Results
- Application of quantum Pinsker inequality to quantum communications
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- Locking and unlocking of quantum nonlocality without entanglement in local discrimination of quantum states