Preservation of entanglement in local noisy channels

TL;DR

This paper investigates how local noisy channels affect entanglement preservation, revealing that certain channels like depolarizing ones completely destroy entanglement, and introduces measures to understand channel biasness and capacity.

Contribution

It introduces biasness measures and analyzes their relation to entanglement capacity, explaining the dependency of entanglement preservation on channel properties.

Findings

Saved entanglement depends on channel type and strength.

Depolarizing channels completely eliminate entanglement.

Biasness measures correlate with entanglement capacity.

Abstract

Entanglement subject to noise can not be shielded against decaying. But, in case of many noisy channels, the degradation can be partially prevented by using local unitary operations. We consider the effect of local noise on shared quantum states and evaluate the amount of entanglement that can be preserved from deterioration. The amount of saved entanglement not only depends on the strength of the channel but also on the type of the channel, and in particular, it always vanishes for the depolarizing channel. The main motive of this work is to analyze the reason behind this dependency of saved entanglement by inspecting properties of the corresponding channels. In this context, we quantify and explore the biasnesses of channels towards the different states on which they act. We postulate that all biasness measures must vanish for depolarizing channels, and subsequently introduce a few measures of biasness. We also consider the entanglement capacities of channels. We observe that the joint behaviour of the biasness quantifiers and the entanglement capacity explains the nature of saved entanglement. Furthermore, we find a pair of upper bounds on saved entanglement which are noticed to imitate the graphical nature of the latter.