Lower bounds for attainable fidelities in entanglement purification

Abstract

We derive lower bounds for the attainable fidelity of standard entanglement purification protocols when local operations and measurements are subjected to errors. We introduce an error parameter which measures the distance between the ideal completely positive map describing a purification step and the one in the presence of errors. We derive nonlinear maps for a lower bound of the fidelity at each purification step in terms of this parameter.