Contraste de hipótesis cuánticas

Laburpena

Hypothesis testing is a fundamental problem in statistical inference and has been a crucial element in the development of information sciences. The Chernoff bound gives the minimal probability of error when discriminating two hypothesis given a large number of observations. Here, we present the quantum counterpart of this problem, i.e, when the hypothesis correspond to two quantum states, thereby solving a longstanding open problem. Remarkably, the expression of the quantum bound is the natural extension of the classical one: the quantum density matrices replace the classical probability distributions. From this bound we obtain a physically meaningful distinguishability measure and the corresponding metric in the space of states. We illustrate these results in the paradigmatic case of qubits