Quantum steering and quantum discord under noisy channels and entanglement swapping

Abstract

Quantum entanglement, quantum discord, and EPR-steering are properties which are considered as valuable resources for fuelling quantum information-theoretic protocols. EPR-steering is a correlation weaker than nonlocality (in the Bell's sense) and yet stronger than entanglement. Quantum discord on the other hand, captures non-classical behaviour beyond that of entanglement, and its study has remained of active research interest during the past two decades. Exploring the behaviour of these quantum correlations in different physical scenarios, like those simulated by open quantum systems, is therefore of crucial importance for understanding their viability for quantum technologies. In this work, we analyse the behaviour of EPR-steering, entanglement, and quantum discord, for partially entangled two-qubit states with coloured noise, introduced by Ameida et al. [1], under various quantum processes. First, we consider the three noisy channel scenarios of; phase damping, generalised amplitude damping and stochastic dephasing channel. Second, we explore their behaviour in an entanglement swapping scenario. We quantify EPR-steering by means of an inequality with three-input two-output measurement settings, and address quantum discord as the interferometric power of quantum states. We discuss the sudden death of steering and entanglement induced by the noisy processes. Additionally, in the case of generalised amplitude damping, a death and revival behaviour can be interpreted in terms of one of the noise's parameters. Second, we contrast the fact that noisy channels in general reduce the amount of correlations present in the system, with the swapping protocol, which displays scenarios where these quantum correlations can be enhanced with respect to the correlations at the initial stage of the protocol. In particular, we present a trade-off between the post-swap amount of correlations and their probability of occurrence.