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

Physical Review A

Comment on “Secret-key-assisted private classical communication capacity over quantum channels”

Mark M. Wilde

Published Apr 29, 2011• 7 citations
Publisher

Abstract

The paper of Hsieh, Luo, and Brun (HLB) [Phys. Rev. A 78, 042306 (2008)] contains several issues with the capacity theorem presented there, one of which is the suggestion that a sender and receiver can achieve entanglement-assisted classical capacity without any entanglement at all, and another of which is a violation of the Holevo bound. There is also an issue with the converse proof of the capacity theorem. In this comment, I point out these issues and provide revisions of the capacity theorem and the converse proof.

DOI
10.1103/physreva.83.046303

Related papers

Secret-key-assisted private classical communication capacity over quantum channels

Min-Hsiu Hsieh, Zhicheng Luo, Todd A. Brun

We prove a regularized formula for the secret-key-assisted capacity region of a quantum channel for transmitting private classical information. This result parallels the work of Devetak et al. (e-print arXiv:quant-ph/0512015) on entanglement-assisted quantum communication capacity . This formula provides a family protocol, the private father protocol, under the resource inequality framework that includes private classical communication without secret-key assistance as a child protocol.

arXiv:0806.3525•Physical Review A•Oct 8, 2008•17 citations

Coding Theorems for Hybrid Channels. II

A. A. Kuznetsova, Alexander Semenovich Holevo

The present paper continues investigation of the capacities of measurement (quantum-classical) channels in the most general setting, initiated in [A. A. Kuznetsova and A. S. Holevo, Theory Probab. Appl., 58 (2014), pp. 264--285]. The proof of coding theorems is given for the classical capacity and entanglement-assisted classical capacity of the measurement channel with arbitrary output alphabet, without assuming that the channel is given by a bounded operator-valued density.

arXiv:1408.3255•Theory of Probability and Its Applications•Jan 1, 2015•5 citations

Private Classical Communication

Mark M. Wilde

We have now seen in Chapters 20–22 how Alice can communicate classical or quantum information to Bob, perhaps even with the help of shared entanglement. One might argue that these communication tasks are the most fundamental tasks in quantum Shannon theory, given that they have furthered our understanding of the nature of information transmission over quantum channels. However, when discussing the communication of classical information, we made no stipulation as to whether this classical information should be public, so that any third party might have partial or full access to it, or private, so that no third party has access. This chapter establishes the private classical capacity theorem, which gives the maximum rate at which Alice can communicate classical information privately to Bob without anyone else in the universe knowing what she sent to him. A variation of the information-processing task corresponding to this theorem was one of the earliest studied in quantum information theory, with the Bennett– Brassard-84 quantum key distribution protocol being the first proposed protocol for exploiting quantum mechanics to establish a shared secret key between two parties. The private classical capacity theorem is important for quantum key distribution because it establishes the maximum rate at which two parties can generate a shared secret key. Another equally important, but less obvious utility of private classical communication is in establishing a protocol for quantum communication at the coherent information rate. Section 22.2 demonstrated a somewhat roundabout way of arriving at the conclusion that it is possible to communicate quantum information reliably at the coherent information rate—recall that we “coherified” the entanglement-assisted classical capacity theorem and then exploited the coherent communication identity and catalytic use of entanglement. Establishing achievability of the coherent information rate via private classical coding is another way of arriving at the same result, with the added benefit that the resulting protocol does not require the catalytic use of entanglement. The intuition for quantum communication via privacy arises from the nocloning theorem. Suppose that Alice is able to communicate private classical messages to Bob, so that the channel's environment (Eve) is not able to distinguish which message Alice is transmitting to Bob.

Cambridge University Press eBooks•Nov 2, 2016•2 citations

Entanglement-assisted quantum communication beating the quantum Singleton bound

Markus Grassl

Brun, Devetak, and Hsieh [Science 314, 436 (2006)] demonstrated that preshared entanglement between the sender and receiver enables quantum communication protocols that have better parameters than schemes without the assistance of entanglement. Subsequently, the same authors derived a version of the so-called quantum Singleton bound that relates the parameters of the entanglement-assisted quantum-error-correcting codes proposed by them. We present an entanglement-assisted quantum communication scheme with parameters violating this bound in certain ranges. For a fixed transmission rate, our scheme allows one to correct a larger fraction of errors.

arXiv:2007.01249•Physical Review A•Feb 24, 2021•62 citations

Entanglement-Assisted Communication Surpassing the Ultimate Classical Capacity

Shuhong Hao, Haowei Shi, Wei Li +2 more

We report experimental entanglement-assisted communication above the ultimate classical capacity set by the Holevo-Schumacher-Westmorel bound. A high-efficiency entanglement source and a phase-conjugate quantum receiver reap the benefit of pre-shared entanglement over lossy and noisy channels.

Conference on Lasers and Electro-Optics•Jan 1, 2021•1 citation

Entanglement-Assisted Communication Surpassing the Ultimate Classical Capacity

Shuhong Hao, Haowei Shi, Wei Li +3 more

We report experimental entanglement-assisted communication above the ultimate classical capacity set by the Holevo-Schumacher-Westmorel bound. A high-efficiency entanglement source and a phase-conjugate quantum receiver reap the benefit of pre-shared entanglement over lossy and noisy channels.

Quantum Information and Measurement (QIM)•Jan 1, 2021•7 citations
The paper of Hsieh, Luo, and Brun (HLB) [Phys. Rev. A 78, 042306 (2008)] contains several issues with the capacity theorem presented there, one of which is the suggestion that a sender and receiver can achieve entanglement-assisted classical capacity without any entanglement at all, and another of which is a violation of the Holevo bound. There is also an issue with the converse proof of the capacity theorem. In this comment, I point out these issues and provide revisions of the capacity theorem and the converse proof.
We have now seen in Chapters 20–22 how Alice can communicate classical or quantum information to Bob, perhaps even with the help of shared entanglement. One might argue that these communication tasks are the most fundamental tasks in quantum Shannon theory, given that they have furthered our understanding of the nature of information transmission over quantum channels. However, when discussing the communication of classical information, we made no stipulation as to whether this classical information should be public, so that any third party might have partial or full access to it, or private, so that no third party has access. This chapter establishes the private classical capacity theorem, which gives the maximum rate at which Alice can communicate classical information privately to Bob without anyone else in the universe knowing what she sent to him. A variation of the information-processing task corresponding to this theorem was one of the earliest studied in quantum information theory, with the Bennett– Brassard-84 quantum key distribution protocol being the first proposed protocol for exploiting quantum mechanics to establish a shared secret key between two parties. The private classical capacity theorem is important for quantum key distribution because it establishes the maximum rate at which two parties can generate a shared secret key. Another equally important, but less obvious utility of private classical communication is in establishing a protocol for quantum communication at the coherent information rate. Section 22.2 demonstrated a somewhat roundabout way of arriving at the conclusion that it is possible to communicate quantum information reliably at the coherent information rate—recall that we “coherified” the entanglement-assisted classical capacity theorem and then exploited the coherent communication identity and catalytic use of entanglement. Establishing achievability of the coherent information rate via private classical coding is another way of arriving at the same result, with the added benefit that the resulting protocol does not require the catalytic use of entanglement. The intuition for quantum communication via privacy arises from the nocloning theorem. Suppose that Alice is able to communicate private classical messages to Bob, so that the channel's environment (Eve) is not able to distinguish which message Alice is transmitting to Bob.
Brun, Devetak, and Hsieh [Science 314, 436 (2006)] demonstrated that preshared entanglement between the sender and receiver enables quantum communication protocols that have better parameters than schemes without the assistance of entanglement. Subsequently, the same authors derived a version of the so-called quantum Singleton bound that relates the parameters of the entanglement-assisted quantum-error-correcting codes proposed by them. We present an entanglement-assisted quantum communication scheme with parameters violating this bound in certain ranges. For a fixed transmission rate, our scheme allows one to correct a larger fraction of errors.