Minimax strategy in quantum signal detection with inconclusive results
Kenji Nakahira, Kentaro Kato, Tsuyoshi Sasaki Usuda · Physical Review A · 2013
We consider the application of the minimax strategy to discrimination between quantum states with a certain fraction of inconclusive results. An inconclusive minimax solution is defined as the pair of a collection of prior probabilities and a quantum measurement that achieves the minimax probability of a detection error subject to the constraint that the highest probability of an inconclusive result does not exceed a given value. We first show a necessary and sufficient condition for an inconclusive minimax solution, and derive that the problem of obtaining an inconclusive minimax measurement can be expressed as a semidefinite programming problem. We then present a condition under which there exists a solution such that at least one of the prior probabilities is a zero. We finally show that for any state set with a certain symmetry, an inconclusive minimax solution exists having the same symmetry.