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

IEEE Transactions on Information Theory

On compound state and mutual information in quantum information theory (Corresp.)

Makoto Ohya

Published Sep 1, 1983• 126 citations
Publisher

Abstract

A quantum mechanical compound state of an input state and its output state generated through a communication channel is constructed. The mutual information of quantum communication theory is defined by using the compound state, and its fundamental properties are studied.
DOI
10.1109/tit.1983.1056719

Related papers

A study of mutual information in quantum information systems

Bao Guanggui

The mutual information in quantum information systems is defined by using the quantum compound state, and its fundamental properties with an application are studied.

World Congress on Intelligent Control and Automation•Nov 7, 2002•0 citations

A mathematical foundation of quantum information and quantum computer -on quantum mutual entropy and entanglement-

Masanori Ohya

The study of mutual entropy (information) and capacity in classica l system was extensively done after Shannon by several authors like Kolmogor ov and Gelfand. In quantum systems, there have been several definitions of t he mutual entropy for classical input and quantum output. In 1983, the autho r defined the fully quantum mechanical mutual entropy by means of the relati ve entropy of Umegaki, and it has been used to compute the capacity of quant um channel for quantum communication process; quantum input-quantum output. Recently, a correlated state in quantum syatems, so-called quantum entangled state or quantum entanglement, are used to study quntum information, in part icular, quantum computation, quantum teleportation, quantum cryptography. In this paper, we mainly discuss three things below: (1) We point out the di fference between the capacity of quantum channel and that of classical-quant um-classical channel. (2) So far the entangled state is merely defined as a non-separable state, we give a wider definition of the entangled state and c lassify the entangled states into three categories. (3) The quantum mutual e ntropy for an entangled state is discussed. The above (2) and (3) are a join t work with Belavkin.

arXiv:quant-ph/9808051•Aug 26, 1998•6 citations

On Quantum Entropies for the Compound Quantum Channel

Noboru Watanabe

In classical information theory, the most important theorems are the coding theorems, which were discussed by calculating the mean entropy and the mean mutual entropy defined by the classical dynamical entropy (Kolmogorov–Sinai). The quantum dynamical entropy was first studied by Emch [13] and Connes–Stormer [11]. After that, several approaches for introducing the quantum dynamical entropy were proposed [10,[Formula: see text]3,[Formula: see text]8,[Formula: see text]39,[Formula: see text]15,[Formula: see text]44,[Formula: see text]9,[Formula: see text]27,[Formula: see text]28,[Formula: see text]2,[Formula: see text]19,[Formula: see text]45]. The efficiency of information transmission for the quantum processes is investigated by using the von Neumann entropy [22] and the Ohya mutual entropy [24]. These entropies were extended to S-mixing entropy by Ohya [26,[Formula: see text]27] in general quantum systems. The mean entropy and the mean mutual entropy for the quantum dynamical systems were introduced based on the S-mixing entropy. In this paper, based on research into the dynamical entropy and mean mutual entropy of quantum systems, this study investigates the characteristics of quantum channels that exhibit entanglement, a property unique to quantum systems, and investigates the behaviour of quantum entropy for compound quantum channels by changing the perspective from information transmission between input and output to a new perspective of information transmission from the initial state to the final state.

Open Systems & Information Dynamics•Mar 1, 2026•0 citations

Construction and analysis of a mathematical model in quantum communication processes

Masanori Ohya, Noboru Watanabe, Regular Members

Abstract The communication of information by means of laser is an important technique. Therefore, it is necessary to construct a communication theory (quantum information theory) including quantum effects of laser action. Ohya, one of the authors, has studied the quantum communication channel and constructed a compound state for systematic formulation of the mutual information in quantum systems. In this paper, (1) we briefly review the mathematical formulation of quantum communication theory and (2) construct a physical model of the optical fiber communication process in order to examine the qualitative properties of the communication channel.

Electronics and Communications in Japan (Part I Communications)•Feb 1, 1985•33 citations

An Entropy Based Treatment of Gaussian Communication Process for General Quantum Systems

Noboru Watanabe

The quantum entropy introduced by von Neumann around 1932 describes the amount of information of the quantum state itself. It was extended by Ohya for C*-systems before Conne-Narnhoffer-Thirring (CNT) entropy. The quantum relative entropy was first defined by Umegaki for σ-finite von Neumann algebras and it was subsequently extended by Araki and Uhlmann for general von Neumann algebras and *-algebras, respectively. By introducing a new notion, the so-called compound state, in 1983 Ohya succeeded to construct the mutual entropy in a complete quantum mechanical system (i.e., input state, output state and channel are all quantum mechanical) describing the amount of information correctly transmitted through the quantum channel. In this paper, we briefly review Ohya's S-mixing entropy and the quantum mutual entropy for general quantum systems. Based on a concept of structure equivalent, we apply the general framework of quantum communication to the Gaussian communication processes.

Open Systems & Information Dynamics•Sep 1, 2013•1 citation

A Note on Entropies for Compound Systems

Noboru Watanabe

In quantum compound systems, joint (or compound) states usually do not exist [26]. The so-called Ohya compound state was defined by using the von Neumann–Schatten decomposition [23] of an input state and a quantum communication channel. Quantum mutual entropy [10] was introduced by using quantum relative entropy [24] between the Ohya compound state and the trivial (product) compound state on the compound (input and output) system. One of the remarkable results related to state entanglement is the Jamiolkowski isomorphism [5]. In this paper, we use the Jamiolkowski isomorphism for the construction of Ohya compound state and we discuss the existence of a completely positive map between compound entangled states and the Ohya compound states. The efficiency of information transmission is investigated by using the mean entropy and the mean mutual entropy [12, 6] of a connected channel.

Open Systems & Information Dynamics•Jun 1, 2015•8 citations
The study of mutual entropy (information) and capacity in classica l system was extensively done after Shannon by several authors like Kolmogor ov and Gelfand. In quantum systems, there have been several definitions of t he mutual entropy for classical input and quantum output. In 1983, the autho r defined the fully quantum mechanical mutual entropy by means of the relati ve entropy of Umegaki, and it has been used to compute the capacity of quant um channel for quantum communication process; quantum input-quantum output. Recently, a correlated state in quantum syatems, so-called quantum entangled state or quantum entanglement, are used to study quntum information, in part icular, quantum computation, quantum teleportation, quantum cryptography. In this paper, we mainly discuss three things below: (1) We point out the di fference between the capacity of quantum channel and that of classical-quant um-classical channel. (2) So far the entangled state is merely defined as a non-separable state, we give a wider definition of the entangled state and c lassify the entangled states into three categories. (3) The quantum mutual e ntropy for an entangled state is discussed. The above (2) and (3) are a join t work with Belavkin.
In classical information theory, the most important theorems are the coding theorems, which were discussed by calculating the mean entropy and the mean mutual entropy defined by the classical dynamical entropy (Kolmogorov–Sinai). The quantum dynamical entropy was first studied by Emch [13] and Connes–Stormer [11]. After that, several approaches for introducing the quantum dynamical entropy were proposed [10,[Formula: see text]3,[Formula: see text]8,[Formula: see text]39,[Formula: see text]15,[Formula: see text]44,[Formula: see text]9,[Formula: see text]27,[Formula: see text]28,[Formula: see text]2,[Formula: see text]19,[Formula: see text]45]. The efficiency of information transmission for the quantum processes is investigated by using the von Neumann entropy [22] and the Ohya mutual entropy [24]. These entropies were extended to S-mixing entropy by Ohya [26,[Formula: see text]27] in general quantum systems. The mean entropy and the mean mutual entropy for the quantum dynamical systems were introduced based on the S-mixing entropy. In this paper, based on research into the dynamical entropy and mean mutual entropy of quantum systems, this study investigates the characteristics of quantum channels that exhibit entanglement, a property unique to quantum systems, and investigates the behaviour of quantum entropy for compound quantum channels by changing the perspective from information transmission between input and output to a new perspective of information transmission from the initial state to the final state.
Abstract The communication of information by means of laser is an important technique. Therefore, it is necessary to construct a communication theory (quantum information theory) including quantum effects of laser action. Ohya, one of the authors, has studied the quantum communication channel and constructed a compound state for systematic formulation of the mutual information in quantum systems. In this paper, (1) we briefly review the mathematical formulation of quantum communication theory and (2) construct a physical model of the optical fiber communication process in order to examine the qualitative properties of the communication channel.
The quantum entropy introduced by von Neumann around 1932 describes the amount of information of the quantum state itself. It was extended by Ohya for C*-systems before Conne-Narnhoffer-Thirring (CNT) entropy. The quantum relative entropy was first defined by Umegaki for σ-finite von Neumann algebras and it was subsequently extended by Araki and Uhlmann for general von Neumann algebras and *-algebras, respectively. By introducing a new notion, the so-called compound state, in 1983 Ohya succeeded to construct the mutual entropy in a complete quantum mechanical system (i.e., input state, output state and channel are all quantum mechanical) describing the amount of information correctly transmitted through the quantum channel. In this paper, we briefly review Ohya's S-mixing entropy and the quantum mutual entropy for general quantum systems. Based on a concept of structure equivalent, we apply the general framework of quantum communication to the Gaussian communication processes.
In quantum compound systems, joint (or compound) states usually do not exist [26]. The so-called Ohya compound state was defined by using the von Neumann–Schatten decomposition [23] of an input state and a quantum communication channel. Quantum mutual entropy [10] was introduced by using quantum relative entropy [24] between the Ohya compound state and the trivial (product) compound state on the compound (input and output) system. One of the remarkable results related to state entanglement is the Jamiolkowski isomorphism [5]. In this paper, we use the Jamiolkowski isomorphism for the construction of Ohya compound state and we discuss the existence of a completely positive map between compound entangled states and the Ohya compound states. The efficiency of information transmission is investigated by using the mean entropy and the mean mutual entropy [12, 6] of a connected channel.