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/9801012 · Physical Review A

Quantum channels showing superadditivity in classical capacity

Masahide Sasaki, Kentaro Kato, Masayuki Izutsu, Osamu Hirota

Published Jul 1, 1998• 133 citations
arXivHTMLPDF

Abstract

We consider a channel coding for sending classical information through a quantum channel with a given ensemble of quantum states (letter states). As is well known, it is generically possible in a quantum channel that the transmittable information in block coding of length $n$ can exceed $n$ times the maximum amount that can be sent without any coding scheme. This so-called superadditivity in classical capacity of a quantum channel is a distinct feature that cannot be found in a classical memoryless channel. In this paper, a practical model of channel coding that shows this property is presented. It consists of a simple code-word selection and the optimum decoding of the code words minimizing the average error probability. At first, optimization of decoding strategy is discussed. Then the channel coding that shows the superadditivity in classical capacity is demonstrated.

DOI
10.1103/physreva.58.146

Related papers

Superadditivity of quantum channel coding rate with finite blocklength quantum measurements

Hye Won Chung, Saikat Guha, Lizhong Zheng

We investigate superadditivity in the maximum achievable rate of reliable classical communication over a quantum channel. The maximum number of classical information bits extracted per use of the quantum channel strictly increases as the number of channel outputs jointly measured at the receiver increases. This phenomenon is called superadditivity. We provide an explanation of this phenomenon by comparing a quantum channel with a classical discrete memoryless channel (DMC) under concatenated codes. We also give a lower bound on the maximum accessible information per channel use at a finite length of quantum measurements in terms of V, which is the quantum version of channel dispersion, and C, the classical capacity of the quantum channel.

IEEE International Symposium on Information Theory (ISIT)•Jun 1, 2014•6 citations

Superadditivity of Quantum Channel Coding Rate With Finite Blocklength Joint Measurements

Hye Won Chung, Saikat Guha, Lizhong Zheng

The maximum rate at which classical information can be reliably transmitted per use of a quantum channel strictly increases in general with N , the number of channel outputs that are detected jointly by the quantum joint-detection receiver (JDR). This phenomenon is known as superadditivity of the maximum achievable information rate over a quantum channel. We study this phenomenon for a pure-state classical-quantum channel and provide a lower bound on C[subscript N]/N, the maximum information rate when the JDR is restricted to making joint measurements over no more than N quantum channel outputs, while allowing arbitrary classical error correction. We also show the appearance of a superadditivity phenomenon-of mathematical resemblance to the aforesaid problem-in the channel capacity of a classical discrete memoryless channel when a concatenated coding scheme is employed, and the inner decoder is forced to make hard decisions on N-length inner codewords. Using this correspondence, we develop a unifying framework for the above two notions of superadditivity, and show that for our lower bound to C[subscript N]/N to be equal to a given fraction of the asymptotic capacity C of the respective channel, N must be proportional to V/C², where V is the respective channel dispersion quantity.

•Aug 1, 2016•8 citations

Classical information capacity of a quantum channel

Paul A. Hausladen, Richard Jozsa, Benjamin W. Schumacher +2 more

We consider the transmission of classical information over a quantum channel. The channel is defined by an ``alphabet'' of quantum states, e.g., certain photon polarizations, together with a specified set of probabilities with which these states must be sent. If the receiver is restricted to making separate measurements on the received ``letter'' states, then the Kholevo theorem implies that the amount of information transmitted per letter cannot be greater than the von Neumann entropy H of the letter ensemble. In fact the actual amount of transmitted information will usually be significantly less than H. We show, however, that if the sender uses a block coding scheme consisting of a choice of code words that respects the a priori probabilities of the letter states, and the receiver distinguishes whole words rather than individual letters, then the information transmitted per letter can be made arbitrarily close to H and never exceeds H. This provides a precise information-theoretic interpretation of von Neumann entropy in quantum mechanics. We apply this result to ``superdense'' coding, and we consider its extension to noisy channels. \textcopyright{} 1996 The American Physical Society.

Physical Review A•Sep 1, 1996•497 citations

Superadditivity of Quantum Channel Coding Rate With Finite Blocklength Joint Measurements

Hye Won Chung, Saikat Guha, Lizhong Zheng

The maximum rate at which classical information can be reliably transmitted per use of a quantum channel strictly increases in general with N , the number of channel outputs that are detected jointly by the quantum joint-detection receiver (JDR). This phenomenon is known as superadditivity of the maximum achievable information rate over a quantum channel. We study this phenomenon for a pure-state classical-quantum channel and provide a lower bound on CN/N, the maximum information rate when the JDR is restricted to making joint measurements over no more than N quantum channel outputs, while allowing arbitrary classical error correction. We also show the appearance of a superadditivity phenomenon-of mathematical resemblance to the aforesaid problem-in the channel capacity of a classical discrete memoryless channel when a concatenated coding scheme is employed, and the inner decoder is forced to make hard decisions on N -length inner codewords. Using this correspondence, we develop a unifying framework for the above two notions of superadditivity, and show that for our lower bound to CN/N to be equal to a given fraction of the asymptotic capacity C of the respective channel, N must be proportional to V/C2, where V is the respective channel dispersion quantity.

arXiv:1310.3793•IEEE Transactions on Information Theory•Aug 2, 2016•8 citations

Superadditivity of quantum channel coding rate with finite blocklength quantum measurements

Hye Won Chung, Lizhong Zheng

This paper investigates the superadditivity of the maximum achievable information rate in a quantum channel. The superadditivity is a phenomenon that the maximum accessible information per channel strictly increases as the number of quantum states jointly measured increases. We give an explanation of this phenomenon by comparing the quantum channel with the classical discrete memoryless channel (DMC) under the concatenated codes, and give a lower bound on the maximum accessible information per channel at a finite length of quantum measurements in terms of V , which is the quantum version of channel dispersion, and C, the capacity of the quantum channel.

Allerton Conference on Communication, Control, and Computing•Oct 1, 2013•2 citations

Implementation of generalized quantum measurements: Superadditive quantum coding, accessible information extraction, and classical capacity limit

Masahiro Takeoka, Mikio Fujiwara, Jun Mizuno +1 more

Quantum-information theory predicts that when the transmission resource is doubled in quantum channels, the amount of information transmitted can be increased more than twice by quantum-channel coding technique, whereas the increase is at most twice in classical information theory. This remarkable feature, the superadditive quantum-coding gain, can be implemented by appropriate choices of code words and corresponding quantum decoding which requires a collective quantum measurement. Recently, an experimental demonstration was reported [M. Fujiwara et al., Phys. Rev. Lett. 90, 167906 (2003)]. The purpose of this paper is to describe our experiment in detail. Particularly, a design strategy of quantum-collective decoding in physical quantum circuits is emphasized. We also address the practical implication of the gain on communication performance by introducing the quantum-classical hybrid coding scheme. We show how the superadditive quantum-coding gain, even in a small code length, can boost the communication performance of conventional coding techniques.

arXiv:quant-ph/0306034•Physical Review A•May 26, 2004•23 citations
We consider a channel coding for sending classical information through a quantum channel with a given ensemble of quantum states (letter states). As is well known, it is generically possible in a quantum channel that the transmittable information in block coding of length nnn can exceed nnn times the maximum amount that can be sent without any coding scheme. This so-called superadditivity in classical capacity of a quantum channel is a distinct feature that cannot be found in a classical memoryless channel. In this paper, a practical model of channel coding that shows this property is presented. It consists of a simple code-word selection and the optimum decoding of the code words minimizing the average error probability. At first, optimization of decoding strategy is discussed. Then the channel coding that shows the superadditivity in classical capacity is demonstrated.
We investigate superadditivity in the maximum achievable rate of reliable classical communication over a quantum channel. The maximum number of classical information bits extracted per use of the quantum channel strictly increases as the number of channel outputs jointly measured at the receiver increases. This phenomenon is called superadditivity. We provide an explanation of this phenomenon by comparing a quantum channel with a classical discrete memoryless channel (DMC) under concatenated codes. We also give a lower bound on the maximum accessible information per channel use at a finite length of quantum measurements in terms of V, which is the quantum version of channel dispersion, and C, the classical capacity of the quantum channel.
The maximum rate at which classical information can be reliably transmitted per use of a quantum channel strictly increases in general with N , the number of channel outputs that are detected jointly by the quantum joint-detection receiver (JDR). This phenomenon is known as superadditivity of the maximum achievable information rate over a quantum channel. We study this phenomenon for a pure-state classical-quantum channel and provide a lower bound on C[subscript N]/N, the maximum information rate when the JDR is restricted to making joint measurements over no more than N quantum channel outputs, while allowing arbitrary classical error correction. We also show the appearance of a superadditivity phenomenon-of mathematical resemblance to the aforesaid problem-in the channel capacity of a classical discrete memoryless channel when a concatenated coding scheme is employed, and the inner decoder is forced to make hard decisions on N-length inner codewords. Using this correspondence, we develop a unifying framework for the above two notions of superadditivity, and show that for our lower bound to C[subscript N]/N to be equal to a given fraction of the asymptotic capacity C of the respective channel, N must be proportional to V/C², where V is the respective channel dispersion quantity.
We consider the transmission of classical information over a quantum channel. The channel is defined by an ``alphabet'' of quantum states, e.g., certain photon polarizations, together with a specified set of probabilities with which these states must be sent. If the receiver is restricted to making separate measurements on the received ``letter'' states, then the Kholevo theorem implies that the amount of information transmitted per letter cannot be greater than the von Neumann entropy H of the letter ensemble. In fact the actual amount of transmitted information will usually be significantly less than H. We show, however, that if the sender uses a block coding scheme consisting of a choice of code words that respects the a priori probabilities of the letter states, and the receiver distinguishes whole words rather than individual letters, then the information transmitted per letter can be made arbitrarily close to H and never exceeds H. This provides a precise information-theoretic interpretation of von Neumann entropy in quantum mechanics. We apply this result to ``superdense'' coding, and we consider its extension to noisy channels. \textcopyright{} 1996 The American Physical Society.
The maximum rate at which classical information can be reliably transmitted per use of a quantum channel strictly increases in general with N , the number of channel outputs that are detected jointly by the quantum joint-detection receiver (JDR). This phenomenon is known as superadditivity of the maximum achievable information rate over a quantum channel. We study this phenomenon for a pure-state classical-quantum channel and provide a lower bound on CN/N, the maximum information rate when the JDR is restricted to making joint measurements over no more than N quantum channel outputs, while allowing arbitrary classical error correction. We also show the appearance of a superadditivity phenomenon-of mathematical resemblance to the aforesaid problem-in the channel capacity of a classical discrete memoryless channel when a concatenated coding scheme is employed, and the inner decoder is forced to make hard decisions on N -length inner codewords. Using this correspondence, we develop a unifying framework for the above two notions of superadditivity, and show that for our lower bound to CN/N to be equal to a given fraction of the asymptotic capacity C of the respective channel, N must be proportional to V/C2, where V is the respective channel dispersion quantity.
This paper investigates the superadditivity of the maximum achievable information rate in a quantum channel. The superadditivity is a phenomenon that the maximum accessible information per channel strictly increases as the number of quantum states jointly measured increases. We give an explanation of this phenomenon by comparing the quantum channel with the classical discrete memoryless channel (DMC) under the concatenated codes, and give a lower bound on the maximum accessible information per channel at a finite length of quantum measurements in terms of V , which is the quantum version of channel dispersion, and C, the capacity of the quantum channel.
Quantum-information theory predicts that when the transmission resource is doubled in quantum channels, the amount of information transmitted can be increased more than twice by quantum-channel coding technique, whereas the increase is at most twice in classical information theory. This remarkable feature, the superadditive quantum-coding gain, can be implemented by appropriate choices of code words and corresponding quantum decoding which requires a collective quantum measurement. Recently, an experimental demonstration was reported [M. Fujiwara et al., Phys. Rev. Lett. 90, 167906 (2003)]. The purpose of this paper is to describe our experiment in detail. Particularly, a design strategy of quantum-collective decoding in physical quantum circuits is emphasized. We also address the practical implication of the gain on communication performance by introducing the quantum-classical hybrid coding scheme. We show how the superadditive quantum-coding gain, even in a small code length, can boost the communication performance of conventional coding techniques.