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 Guassian channels.