Entanglement Fidelity in Standard Quantum Channels

2026-03-08

AI Summary

This study investigates the capacity of standard quantum channels to preserve entanglement between a system and its reference during transmission. Building upon Schumacher’s Kraus operator formalism and employing a two-symbol parametrized source model, the authors derive a unified closed-form expression for entanglement fidelity applicable to any completely positive trace-preserving (CPTP) map with a finite Kraus representation. For the first time, explicit analytical formulas are provided for canonical channels—including Pauli-X, dephasing, depolarizing, Werner–Holevo, generalized Pauli (Weyl), and amplitude damping channels—revealing how joint source–channel parameters influence entanglement preservation. The resulting framework enables direct comparison and ranking of channel performance under typical input states.

Technology Category

• Machine Learning: Quantum Machine Learning
• Planning, Routing, and Scheduling: Scheduling under Uncertainty
• Constraint Satisfaction and Optimization: Satisfiability

Application Category

• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics

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.

Problem

• entanglement fidelity
• quantum channels
• quantum noise models
• CPTP maps
• quantum communication

Innovation

• entanglement fidelity
• quantum channels
• Kraus operators
• closed-form expressions
• CPTP maps