We study the performances of quantum channel adaptive [4,1] code transmitting in a joint amplitude damping and dephasing channel, the [6,2] code transmitting in an amplitude damping channel by combining the encoding, noise process, and decoding as one effective channel. We explicitly obtain the entanglement fidelities. The recovery operators of the [6,2] code are given. The performance is nearly optimal compared with that of the optimal method of semidefinite programming.

Chinese Physics BJan 1, 20134 citations

Entanglement-enhanced transmission of classical information in Pauli channels with memory: Exact solution

D. Daems

arXiv:quant-ph/0610165Physical Review AJul 12, 200743 citations

International Conference on Quantum Communications, Networking, and Computing (QCNC)

Entanglement Fidelity in Standard Quantum Channels

Niccolò Zanieri, Marios Kountouris

Published Apr 6, 2026• 0 citations

Publisher

Abstract

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 for any completely positive trace-preserving 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.

DOI: 10.1109/qcnc69040.2026.00121

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Entanglement Fidelity in Standard Quantum Channels

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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.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.

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For example, depolarizing channels are \n important quantum channels, but do not have tight numerical bounds. \nWe obtain upper bounds on the quantum capacity of some unital and non-unital channels \n -- two-qubit Pauli channels, two-qubit depolarizing channels, two-qubit locally symmetric channels, \n shifted qubit depolarizing channels, and shifted two-qubit Pauli channels -- \n using the coherent information of some degradable channels. We use the notion \n of twirling quantum channels, and Smith and Smolin's method of constructing \n degradable extensions of quantum channels extensively. The degradable channels we \n introduce, study and use are two-qubit amplitude damping channels. 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Entanglement fidelity of channel adaptive quantum codes

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Chinese Physics BJan 1, 20134 citations

Entanglement-enhanced transmission of classical information in Pauli channels with memory: Exact solution

D. Daems

The amount of classical information that is reliably transmitted over two uses of general Pauli channels with memory, modeled as a correlated noise between a single pair of uses, is investigated. The maximum of the mutual information between the input and the output is proven to be achieved by a class of product states that is explicitly given in terms of the relevant channel parameters below some memory threshold, and by maximally entangled states above this threshold. In particular, this proves a conjecture on the depolarizing channel by Macchiavello and Palma [Phys. Rev. A 65, 050301(R) (2002)]. Furthermore, it also shows that no other scenario can occur for Pauli channels as for example the existence of an intermediate optimal degree of entanglement reported for some Gaussian channels with memory.The amount of classical information that is reliably transmitted over two uses of general Pauli channels with memory, modeled as a correlated noise between a single pair of uses, is investigated. The maximum of the mutual information between the input and the output is proven to be achieved by a class of product states that is explicitly given in terms of the relevant channel parameters below some memory threshold, and by maximally entangled states above this threshold. In particular, this proves a conjecture on the depolarizing channel by Macchiavello and Palma [Phys. Rev. A 65, 050301(R) (2002)]. Furthermore, it also shows that no other scenario can occur for Pauli channels as for example the existence of an intermediate optimal degree of entanglement reported for some Gaussian channels with memory.

arXiv:quant-ph/0610165Physical Review AJul 12, 200743 citations

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}

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.