Entangling power and fidelity diagnostic for bipartite quantum channels

Abstract

We study two complementary diagnostics of bipartite quantum channels, namely fidelity preservation across different classes of input states and entanglement generation from product inputs, given by properly defined entangling power for bipartite channels. We show that the fidelity averaged over any fixed Schmidt-coefficients local-unitary orbit for equal local dimensions is completely determined by average input-output fidelity and its restriction to product inputs. We also introduce concurrence- and negativity-based entangling power for 2-qubit channels, prove their convexity and monotonicity under local postprocessing, and show that, unlike the previously proposed linear-entropy quantity, they vanish for all separable channels. Examples of non-separable channels are investigated. Finally, we generalize our definitions of entangling power to non-product inputs, and provide an analytical lower bound for the concurrence-based entanglement variation, showing its effectiveness with specific examples.