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Electronics and Communications in Japan (Part III Fundamental Electronic Science)

Properties of quantum reliability function and its applications to several quantum signals

Keiko Kurokawa, Osamu Hirota

Published Apr 18, 2001• 3 citations
Publisher

Abstract

Abstract This paper discusses applications of the reliability function to specific problems in connection with communication systems transmitted by means of quantum states. The reliability function and cutoff rate for various quantum optical communication systems are specifically presented. The effects of these characteristics on the limit characteristics in the coding scheme by quantum states. © 2001 Scripta Technica, Electron Comm Jpn Pt 3, 84(9): 31–41, 2001

DOI
10.1002/ecjc.1032

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Abstract This paper discusses applications of the reliability function to specific problems in connection with communication systems transmitted by means of quantum states. The reliability function and cutoff rate for various quantum optical communication systems are specifically presented. The effects of these characteristics on the limit characteristics in the coding scheme by quantum states. © 2001 Scripta Technica, Electron Comm Jpn Pt 3, 84(9): 31–41, 2001
In information theory, the reliability function and its bounds, describing the exponential behavior of the error probability, are important quantitative characteristics of the channel performance. From a more general point of view, these bounds provide certain measures of distinguishability of a given set of classical states. In a previous paper, quantum analogs of the random coding and expurgation lower bounds for the case of pure signal states were introduced. Here we discuss the case of general quantum states, in particular, we prove the expurgation bound conjectured previously and find the quantum cutoff rate for arbitrary mixed signal states.
In information theory the reliability function and its bounds, describing the exponential behavior of the error probability, are the most important quantitative characteristics of the channel performance. From a general point of view, these bounds provide certain measures of distinguishability of a given set of states. In an earlier paper we introduced quantum analogs of the random coding and the expurgation lower bounds for the case of pure signal states. Here we discuss the general case, in particular, we prove the previously conjectured expurgation bound and find the quantum cutoff rate in the case of arbitrary mixed signal states.
Mutual entropy was introduced in classical communication theories to measure how much information can be transmitted from an input system to an output system. It has been expanded to quantum systems and applied to various physical models. By contrast, quantum Markov chains, introduced as an extension of classical Markov chains, have been used to explain the irreversibility of observed systems. In [1], a physical model used frequently in quantum optics was applied to a quantum Markov chain. The Stinespring-Kraus expression was derived to discuss mutual entropy on quantum Markov chains. Mutual entropy was then computed and irreversibility was examined using numerical experiments. To further the ongoing research, mean mutual entropy is applied here to the same quantum Markov chain as the previous one; necessary discussion is included. © 1997 Scripta Technica, Inc. Electron Comm Jpn Pt 3, 80(1): 104–112, 1997
The general quantum communication process, with the optical communication process as its actual model, is strictly formulated mathematically in terms of Ohya's quantum mechanics channel, which describes the state change. Until recently the decay process and the amplifier process have been described as actual communication processes, using the concepts of the channel and its extension, lifting. Based on that description, the error probability and SNP are derived. This paper introduces a new system called the control system into the communication process, and provides the squeezed vacuum state as the quantum state of the system. We examine how conventional communication efficiency can be improved by the squeezed vacuum state, using the error probability. © 1998 Scripta Technica. Electron Comm Jpn Pt 3, 81(7): 18–27, 1998