Quantifying the noise of a quantum channel by noise addition

Abstract

In this paper we introduce a way to quantify the noise level associated to a given quantum transformation. The key mechanism lying at the heart of the proposal is noise addition: in other words we compute the amount of extra noise we need to add to the system through convex combination with a reference noisy map or by reiterative applications of the original map, before the resulting transformation becomes entanglement breaking. We also introduce the notion of entanglement-breaking channels of order $n$ (i.e., maps which become entanglement breaking after $n$ iterations), and the associated notion of amendable channels (i.e., maps which can be prevented from becoming entanglement breaking after iterations by interposing proper quantum transformations). Explicit examples are analyzed in the context of qubit and one-mode Gaussian channels.