Optimal fidelity for a quantum channel may be attained by non-maximally entangled states

TL;DR

This paper demonstrates that optimal fidelity in quantum channels can be achieved using non-maximally entangled states, especially under noisy conditions, challenging the assumption that maximally entangled states are always optimal.

Contribution

It shows that non-maximally entangled states can attain optimal fidelity in noisy quantum channels with minimal processing, revealing new insights into entanglement's role in quantum communication.

Findings

Optimal fidelity is achieved with non-maximally entangled states.

Entanglement can be vanishingly small in very noisy channels.

Local post-processing enhances fidelity only beyond a noise threshold.

Abstract

To establish an entangled state of optimal fidelity between two distant observers when the available quantum channel is noisy, is a central problem in quantum information theory. We consider an instance of this problem for two-qubit systems when only a single use of the channel and local post-processing by trace preserving operations are allowed. We show that the optimal fidelity is obtained only when part of an appropriate non-maximally entangled state is transmitted through the channel. The entanglement of this state can be vanishingly small when the channel becomes very noisy. Moreover, in the optimal case no further local processing is required to enhance the fidelity. We further show that local post-processing can enhance fidelity if and only if the amount of noise is larger than a critical value and entanglement of the transmitted state is bounded from below. A notable consequence of these results is that the ordering of states under an entanglement monotone can be reversed even when the states undergo the same local interaction via a trace-preserving completely positive map.