Generalized Holevo theorem and distinguishability notions

Abstract

We present a generalization of the Holevo theorem through distance measures between quantum states, showing that each of these leads to an alternative Holevo theorem. This result involves two quantities: the distance-based Holevo quantity and the generalized accessible information I d. Additionally, we consider three distinguishability notions relevant to quantum cryptography, applying the resulting new inequalities to qubits ensembles. For some well-known distinguishability notion, we show that for any ensemble of two qubits the generalized quantities - I d and - are equal. On the other hand, by using a paradigmatic example, we show that the quantities corresponding to the Bures distance captures not only the non-commutativity of the ensemble but also its purity.