Quantifying the entanglement of quantum channel

Abstract

To describe the nonclassicality of quantum channels, it is necessary to quantify their properties. In the framework of resource theory of quantum channel, we present three new entanglement measures of channels for a quantum system of arbitrary finite dimension, based on the Choi relative entropy of channels, concurrence, and k-ME concurrence, respectively. Rigorous proofs show that these proposed measures fulfill all the requirements dictated by the resource theory of quantum channels, including non-negativity, weak monotonicity, strong monotone, convexity, additivity, and subadditivity. By using the measure, we describe the probability that the initial hypothesis is true in the hypothesis testing of channels. Compared with other known measures of the quantum channels, these measures have an obvious advantage in computability. According to the power of generating entanglement, we give a classification of quantum channels. Moreover, we provide several examples that characterize the properties of quantum channels and the conversions between quantum coherence states and entangled states and between fully separable states and multipartite entangled states.