Entanglement Fidelity in Standard Quantum Channels

TL;DR

This paper derives explicit formulas for entanglement fidelity in various standard quantum noise channels, aiding in assessing and comparing their ability to preserve quantum correlations.

Contribution

It provides closed-form, channel-agnostic expressions for entanglement fidelity across multiple quantum noise models using Kraus operators.

Findings

Explicit formulas for entanglement fidelity in several quantum channels.

Dependence of fidelity on input states and channel parameters.

Enables comparison and ranking of quantum channels based on fidelity.

Abstract

Entanglement fidelity quantifies how well a quantum channel preserves the correlations between a transmitted system and an inaccessible reference system. We derive closed-form expressions for the entanglement fidelity associated with several standard quantum noise models, including the random Pauli-X, dephasing, depolarizing, Werner-Holevo, generalized Pauli (Weyl), and amplitude-damping channels. For each model, we express the entanglement fidelity in terms of a general input density operator $\rho$, using Schumacher's Kraus-operator approach, which provides a channel-agnostic recipe applicable to any completely positive trace-preserving (CPTP) map with a finite Kraus representation. We then specialize to a communication scenario in which the source emits a two-letter parametric alphabet, thereby making explicit the dependence of entanglement preservation on both channel and source parameters. The resulting expressions enable direct comparisons of channel performance and rankings for representative families of input states, including common qubit states.