Coherent information

About: Coherent information is a research topic. Over the lifetime, 1225 publications have been published within this topic receiving 46672 citations.

Quantum Information Theory: Results and Open Problems

Abstract: The discipline of information theory was founded by Claude Shannon in a truly remarkable paper [Sh] which laid down the foundations of the subject. We begin with a quote from this paper which is an excellent summary of the main concern of information theory: The fundamental problem of communication is that of reproducing at one point either exactly or approximately a message selected at another point.

Quantum reconstruction of the mutual coherence function.

Abstract: Light is a major carrier of information about the world around us, from the microcosmos to the macrocosmos. The present methods of detection are sensitive both to robust features, such as intensity, or polarization, and to more subtle effects, such as correlations. Here we show how wave front detection, which allows for registering the direction of the incoming wave flux at a given position, can be used to reconstruct the mutual coherence function when combined with some techniques previously developed for quantum information processing.

Fisher Information of Wavefunctions: Classical and Quantum

Abstract: A parametric quantum mechanical wavefunction naturally induces parametric probability distributions by taking absolute square, and we can consider its classical Fisher information. On the other hand, it also induces parametric rank-one projections which may be viewed as density operators, and we can talk about its quantum Fisher information. Among many versions of quantum Fisher information, there are two prominent ones. The first, defined via a quantum score function, was introduced by Helstrom in 1967 and is well known. The second, defined via the square root of the density operator, has its origin in the skew information introduced by Wigner and Yanase in 1963 and remains relatively unnoticed. This study is devoted to investigating the relationships between the classical Fisher information and these two versions of quantum Fisher information for wavefunctions. It is shown that the two versions of quantum Fisher information differ by a factor 2 and that they dominate the classical Fisher information. The non-coincidence of these two versions of quantum Fisher information may be interpreted as a manifestation of quantum discord. We further calculate the difference between the Helstrom quantum Fisher information and the classical Fisher information, and show that it is precisely the instantaneous phase fluctuation of the wavefunctions.

Information content of coherent images

Abstract: Information theory, as developed by Shannon (1948), provides a theoretical framework for describing the transfer of information through a communication channel. A coherent imaging system is a particular form of communication channel which is characterized by a multiplicative noise process termed 'speckle'. Information theory is used to assess the effect of speckle on the information content of coherent images. Particular emphasis is given to relating information theoretic concepts to intuitive descriptions of information based on physical models.

Entropy in operational statistics and quantum logic

Abstract: In a series of recent papers, Randall and Foulis have developed a generalized theory of probability (operational statistics) which is based on the notion of a physical operation. They have shown that the quantum logic description of quantum mechanics can be naturally imbedded into this generalized theory of probability. In this paper we shall investigate the role of entropy (in the sense of Shannon's theory of information) in operational statistics. We shall find that there are several related entropy concepts in operational statistics. We shall examine the relationships between these different entropy concepts and examine their implications for the foundations of quantum theory. We shall also examine the extension of the Jaynes inference scheme to the operational statistics formalism, and apply the latter to the case of quantum statistical mechanics.