Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:quant-ph/0211093 · Physical Review A

Holevo-Schumacher-Westmoreland channel capacity for a class of qudit unital channels

John A. Cortese

Published Feb 4, 2004• 46 citations
arXivHTMLPDF

Abstract

Using the unique nature of the average output state of an optimal signalling ensemble, we prove that for a special class of qudit unital channels, the Holevo-Schumacher-Westmoreland channel capacity is $\mathcal{C}={\mathrm{log}}_{2}(d)\ensuremath{-}{\mathrm{min}}_{\ensuremath{\rho}}\mathcal{S}(\mathcal{E}(\ensuremath{\rho})),$ where d is the dimension of the qudit. The result is extended to products of the same class of unital qudit channels. Thus, the connection between the minimum von Neumann entropy at the channel output and the transmission rate for classical information over quantum channels extends beyond the qubit domain.

DOI
10.1103/physreva.69.022302

Related papers

Relative Entropy and Single Qubit Holevo-Schumacher-Westmoreland Channel Capacity

John A. Cortese

The relative entropy description of Holevo-Schumacher-Westmoreland (HSW) classical channel capacity is applied to single qubit channels. A simple formula for the relative entropy of qubit density matrices in the Bloch sphere representation is derived. This formula is combined with the King-Ruskai-Szarek-Werner qubit channel ellipsoid picture to analyze several unital and non-unital qubit channels in detail. An alternate proof that the optimal HSW signalling states for single qubit unital channels are those states with the minimum channel output entropy is presented. The derivation is based on the symmetries of the qubit relative entropy formula and the King-Ruskai-Szarek-Werner qubit channel ellipsoid picture. A proof is given that the average output density matrix of any set of optimal HSW signalling states for a (qubit or non-qubit) quantum channel is unique.

arXiv:quant-ph/0207128•Jul 22, 2002•5 citations

THE HSW CHANNEL CAPACITY FOR THE DIAGONAL UNITAL QUDIT CHANNELS

Yu-Chun Wu, Zheng-Wei Zhou, Guang‐Can Guo

The Holevo–Schumacher–Westermoreland (HSW) channel capacity for the diagonal unital qudit channels is considered. In Phys. Rev.A69, 022302, the HSW channel capacity for the diagonal unital qudit channels Φ is given as χ(Φ)=1- min ρH(Φ(ρ)), where minimization is over the input states of the channel. In this paper, using the concavity of von Neumann entropy, we show that using only pure states we can work out its HSW channel capacity. Hence, our result simplifies the computation.

International Journal of Quantum Information•Dec 1, 2004•0 citations

Quantum Information Theory: Classical Communication Over Quantum Channels

John A. Cortese

This thesis studies classical communication over quantum channels. Chapter 1 describes an algebraic technique which extends several previously known qubit channel capacity results to the qudit quantum channel case. Chapter 2 derives a formula for the relative entropy function of two qubit density matrices in terms of their Bloch vectors. The application of the Bloch vector relative entropy formula to the determination of Holevo-Schumacher-Westmoreland (HSW) capacities for qubit quantum channels is discussed. Chapter 3 outlines several numerical simulation results which support theoretical conclusions and conjectures discussed in Chapters 1 and 2. Chapter 4 closes the thesis with comments, examples and discussion on the additivity of Holevo Chi and the HSW channel capacity.

•Feb 18, 2004•4 citations

Remark on the HSW Channel Capacityfor the Qubit Unital Channel

Guang-Can Guo

The Holevo-Schumacher-Westermoreland (HSW) channel capacity for the qudit unital channels was considered. A simpler formula for computing HSW channel capacity was given. And the HSW channel capacity can be determined by using only pure states. This result simplifies the computation of HSW channel capacity for the qudit unital channel.

•Jan 1, 2004•0 citations

Additivity of the Classical Capacity of Entanglement-Breaking Quantum Channels

Peter W. Shor

We show that for the tensor product of an entanglement-breaking quantum channel with an arbitrary quantum channel, both the minimum entropy of an output of the channel and the Holevo-Schumacher-Westmoreland capacity are additive. In addition, for the tensor product of two arbitrary quantum channels, we give a bound involving entanglement of formation for the amount of subadditivity (for minimum entropy output) or superadditivity (for classical capacity) that can occur. One of the more important open questions of quantum information theory is the determination of the capacity of a quantum channel for carrying classical information. This question has been only partially resolved. If entanglement between multiple inputs to the channel is not allowed, a formula for the classical capacity of a quantum channel has indeed been discovered [1, 2]. This capacity formula for a quantum channel Ψ is χ ∗ (Ψ) = max p i,ρ i H Ψ(piρi) − ∑

•Jan 1, 2002•157 citations

Additivity of the classical capacity of entanglement-breaking quantum channels

Peter W. Shor

We show that for the tensor product of an entanglement-breaking quantum channel with an arbitrary quantum channel, both the minimum entropy of an output of the channel and the Holevo–Schumacher–Westmoreland capacity are additive. In addition, for the tensor product of two arbitrary quantum channels, we give a bound involving entanglement of formation for the amount of subadditivity (for minimum entropy output) or superadditivity (for classical capacity) that can occur.

arXiv:quant-ph/0201149•Journal of Mathematical Physics•Sep 1, 2002•170 citations
Using the unique nature of the average output state of an optimal signalling ensemble, we prove that for a special class of qudit unital channels, the Holevo-Schumacher-Westmoreland channel capacity is C=log2(d)\ensuremath−min\ensuremathρS(E(\ensuremathρ)),\mathcal{C}={\mathrm{log}}_{2}(d)\ensuremath{-}{\mathrm{min}}_{\ensuremath{\rho}}\mathcal{S}(\mathcal{E}(\ensuremath{\rho})),C=log2​(d)\ensuremath−min\ensuremathρ​S(E(\ensuremathρ)), where d is the dimension of the qudit. The result is extended to products of the same class of unital qudit channels. Thus, the connection between the minimum von Neumann entropy at the channel output and the transmission rate for classical information over quantum channels extends beyond the qubit domain.
The relative entropy description of Holevo-Schumacher-Westmoreland (HSW) classical channel capacity is applied to single qubit channels. A simple formula for the relative entropy of qubit density matrices in the Bloch sphere representation is derived. This formula is combined with the King-Ruskai-Szarek-Werner qubit channel ellipsoid picture to analyze several unital and non-unital qubit channels in detail. An alternate proof that the optimal HSW signalling states for single qubit unital channels are those states with the minimum channel output entropy is presented. The derivation is based on the symmetries of the qubit relative entropy formula and the King-Ruskai-Szarek-Werner qubit channel ellipsoid picture. A proof is given that the average output density matrix of any set of optimal HSW signalling states for a (qubit or non-qubit) quantum channel is unique.
This thesis studies classical communication over quantum channels. Chapter 1 describes an algebraic technique which extends several previously known qubit channel capacity results to the qudit quantum channel case. Chapter 2 derives a formula for the relative entropy function of two qubit density matrices in terms of their Bloch vectors. The application of the Bloch vector relative entropy formula to the determination of Holevo-Schumacher-Westmoreland (HSW) capacities for qubit quantum channels is discussed. Chapter 3 outlines several numerical simulation results which support theoretical conclusions and conjectures discussed in Chapters 1 and 2. Chapter 4 closes the thesis with comments, examples and discussion on the additivity of Holevo Chi and the HSW channel capacity.
We show that for the tensor product of an entanglement-breaking quantum channel with an arbitrary quantum channel, both the minimum entropy of an output of the channel and the Holevo-Schumacher-Westmoreland capacity are additive. In addition, for the tensor product of two arbitrary quantum channels, we give a bound involving entanglement of formation for the amount of subadditivity (for minimum entropy output) or superadditivity (for classical capacity) that can occur. One of the more important open questions of quantum information theory is the determination of the capacity of a quantum channel for carrying classical information. This question has been only partially resolved. If entanglement between multiple inputs to the channel is not allowed, a formula for the classical capacity of a quantum channel has indeed been discovered [1, 2]. This capacity formula for a quantum channel Ψ is χ ∗ (Ψ) = max p i,ρ i H Ψ(piρi) − ∑