The paper analyzes the behavior of quantum channels, particularly in large dimensions, by proving various properties of the quantum gate fidelity. Many of these properties are of independent intere...
The paper analyzes the behavior of quantum channels, particularly in large dimensions, by proving various properties of the quantum gate fidelity. Many of these properties are of independent interest in the theory of distance measures on quantum operations. A non-uniqueness result for the gate fidelity is proven, a consequence of which is the existence of non-depolarizing channels that produce a constant gate fidelity on pure states. Asymptotically, the gate fidelity associated with any quantum channel is shown to converge to that of a depolarizing channel. Methods for estimating the minimum of the gate fidelity are also presented.
Abstract We introduce the concept of quasi-inverse of quantum and classical channels, prove general properties of these inverses and determine them for a large class of channels acting in an arbitrary finite dimension. Therefore we extend the previous results of Karimipour et al (2020 Phys. Rev. A 101 032109) to arbitrary dimensional channels and to the classical domain. We demonstrate how application of the proposed scheme can increase on the average the fidelity between a given random pure state and its image transformed by the quantum channel followed by its quasi-inversion.
Abstract We study the problem of maximizing the Jensen gap with respect to the probability distribution in a fairly general case, and prove a theorem on the optimal distribution. Using the results obtained, we calculate the one-shot capacity of a certain family of non-unital quantum channels. We show that in sufficiently large dimensions the channel admits one of two modes of an optimal input ensemble depending on the parameters. We also prove that both the fulfillment and the violation of the entanglement-breaking property are possible in any dimension depending on the parameters of the channel.