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

Kluwer Academic Publishers eBooks

Superadditivity in Capacity of Quantum Channel by Classical Pseudo-Cyclic Codes

Shogo Usami, Tsuyoshi Sasaki Usuda, Ichi Takumi, Ryohei Nakano, Masayasu Hata

Published Feb 24, 2006• 0 citations
Publisher

Abstract

Analytical solution of mutual information by square-root measurement for binary linear code is given. Applying the solution, we show properties of superadditivity in capacity by BCH codes with codeword length 15 and 31. Furthermore, we refer to codes almost achieving the quantum channel capacity.
DOI
10.1007/0-306-47114-0_7

Related papers

Properties of Quantum Gain of Coding with Information Criterion by Binary Linear Codes

Yuki Ishida, Shogo Usami, Tsuyoshi Sasaki Usuda +1 more

In quantum information theory, there is superadditivity in capacity of a quantum channel as special property. We showed the calculating method of mutual information analytically for binary linear codes by using Square-root measurement as decoding process. Therefore, many examples of codes which shows existence of superadditivity in capacity have been given. But the scope of method was not clarified. In the present paper, we show the method can be applied to any binary linear codes. Moreover, we show quantum channel capacity is almost attained in finite codeword length by using approximation to simplex code.

IEEJ Transactions on Electronics Information and Systems•Jan 1, 2006•5 citations

Properties of quantum gain of coding with information criterion by binary linear codes

Yuki Ishida, Shogo Usami, Tsuyoshi Sasaki Usuda +1 more

Abstract In quantum information theory, superadditivity in the capacity of a quantum channel occurs as a special property. We present a method of calculating the mutual information analytically for binary linear codes by using square‐root measurement as the decoding process. Many examples of codes showing the existence of superadditivity in capacity have been given in the past, but the scope of the method was not clarified. In the present paper, we show that the method can be applied to any binary linear codes. We also show that the quantum channel capacity is almost fully attained in a finite codeword length by using approximation to simplex code. © 2008 Wiley Periodicals, Inc. Electr Eng Jpn, 163(4): 48–57, 2008; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/eej.20646

Electrical Engineering in Japan•Apr 23, 2008•3 citations

Quantum channels showing superadditivity in classical capacity

Masahide Sasaki, Kentaro Kato, Masayuki Izutsu +1 more

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.

arXiv:quant-ph/9801012•Physical Review A•Jul 1, 1998•133 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 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

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
In quantum information theory, there is superadditivity in capacity of a quantum channel as special property. We showed the calculating method of mutual information analytically for binary linear codes by using Square-root measurement as decoding process. Therefore, many examples of codes which shows existence of superadditivity in capacity have been given. But the scope of method was not clarified. In the present paper, we show the method can be applied to any binary linear codes. Moreover, we show quantum channel capacity is almost attained in finite codeword length by using approximation to simplex code.
Abstract In quantum information theory, superadditivity in the capacity of a quantum channel occurs as a special property. We present a method of calculating the mutual information analytically for binary linear codes by using square‐root measurement as the decoding process. Many examples of codes showing the existence of superadditivity in capacity have been given in the past, but the scope of the method was not clarified. In the present paper, we show that the method can be applied to any binary linear codes. We also show that the quantum channel capacity is almost fully attained in a finite codeword length by using approximation to simplex code. © 2008 Wiley Periodicals, Inc. Electr Eng Jpn, 163(4): 48–57, 2008; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/eej.20646
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.
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.
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 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.