Abstract:
In quantum state discrimination, the design of measurement operators and probe states is typically formulated under the assumption that the set of possible states is perfectly known, but this may yield designs that are sensitive to deviations in the realized set of states. For example, the channel through which a transmitted state is sent may not be deterministic, but instead may be characterized by a classical distribution over quantum channels. In this article, we consider the design of measurement schemes and probe states for quantum detection over an uncertain quantum channel. We present stochastic-gradient-based algorithms to maximize the expected performance over the channel distribution under two design scenarios: joint design and two-stage design. We consider various design objectives, including detection probability and mutual information, with the latter leading to a hybrid scheme consisting of a von Neumann measurement and a classical hypothesis test. Furthermore, we introduce a channel discrimination scheme that leverages the isometric extension of a quantum channel, which increases channel distinguishability while simultaneously reducing the effective dimensionality and optimization complexity. In addition, we apply amortized optimization techniques to train a recurrent neural network in order to improve the convergence speed of the proposed algorithms. Finally, we apply the proposed algorithms to multicopy channel discrimination as well as to a novel joint channel–state discrimination scenario.