Sending quantum entanglement through noisy channels

TL;DR

This paper investigates how quantum entanglement behaves when transmitted through noisy channels, focusing on entanglement fidelity and entropy production, and their implications for quantum cryptography and error correction.

Contribution

It introduces and analyzes entanglement fidelity and entropy production as key measures for entanglement transmission through noisy channels, linking them to quantum security and error correction.

Findings

Entanglement fidelity depends only on the initial state and channel evolution.

Entropy production relates to the loss of entanglement during transmission.

The inequalities derived provide insights into quantum cryptography security.

Abstract

This paper addresses some general questions of quantum information theory arising from the transmission of quantum entanglement through (possibly noisy) quantum channels. A pure entangled state is prepared of a pair of systems $R$ and $Q$, after which $Q$ is subjected to a dynamical evolution given by the superoperator $\superop^{Q}$. Two interesting quantities can be defined for this process: the entanglement fidelity $F_{e}$ and the entropy production $S_{e}$. It turns out that neither of these quantities depends in any way on the system $R$, but only on the initial state and dynamical evolution of $Q$. $F_{e}$ and $S_{e}$ are related to various other fidelities and entropies, and are connected by an inequality reminiscent of the Fano inequality of classical information theory. Some insight can be gained from these techniques into the security of quantum cryptographic protocols and the nature of quantum error-correcting codes.