Entanglement Fidelity in Standard Quantum Channels
This work provides explicit formulas for entanglement fidelity, which is crucial for evaluating and comparing the performance of quantum channels in preserving quantum correlations for researchers in quantum information and communication.
This paper derives closed-form expressions for entanglement fidelity across various standard quantum noise models, including random Pauli-X, dephasing, and depolarizing channels. The expressions are provided for a general input density operator and then specialized for a two-letter parametric alphabet, allowing for direct comparison of channel performance.
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 $ρ$, 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.