International Conference on Computing Anticipatory Systems (CASYS)

Information transmission in stationary stochastic systems

Bohdan Hejna, Igor Vajda

Published Jan 1, 1999• 3 citations

Abstract

In the present paper we consider a simple model of stochastic systems, which include basic systems of quantum physics. In the framework of this model we demonstrate the Boltzman entropy, second law of thermodynamics and Gibbs theorem as classical achievements on one side, and several possible entropies of the Shannon theory, and their relations to the Boltzman entropy on the other side. We introduce an information transmission in the systems under consideration, define the Shannon information in a variable about the system state, and formulate the concept of information capacity of a system. We explicitly evaluate the capacity of a system governed by the Bose–Einstein law (a boson channel) and that governed by the Fermi–Dirac law (a fermion channel).

DOI: 10.1063/1.58272

Related papers

Information Capacity of Quantum Transfer Channels and Thermodynamic Analogies

Bohdan Hejna

We will begin with a simple type of stationary stochastic1 systems of quantum physics using them within a frame of the Shannon Information Theory and Thermodynamics but starting with their algebraic representation. Based on this algebraic description a model of information transmission in those systems by defining the Shannon information will be stated in terms of variable about the system state. Measuring on these system is then defined as a spectral decomposition of measured quantities operators. The information capacity formulas, now of the narrow-band nature, are derived consequently, for the simple system governed by the Bose–Einstein (B–E) Law [bosonic (photonic) channel] and that one governed by the Fermi-Dirac (F–D) Law [fermionic (electron) channel]. The not-zero value for the average input energy needed for information transmission existence in F–D systems is stated [11, 12].

InTech eBooksOct 3, 20120 citations

Quantum Developments of Classical Information Theory

Mostafa Mansour

These notes (in French) provide a concise introduction to information theory, spanning its classical foundations: Shannon entropy, joint and conditional entropies, mutual information, statistical correlations, and Markov chains; as well as Shannon's source coding and channel capacity theorems, which govern the optimal compression and transmission of information through noisy channels. They also cover the quantum extensions of these concepts, including the density operator formalism, distances between quantum states, von Neumann entropy, coherent information, conditional entropy, entanglement theory, quantum discord, and quantum resource theory.

Feb 7, 20260 citations

Quantum information II

Vlatko Vedral

Abstract This chapter discusses the principles of quantum information. The quantum mechanical equivalent of the Shannon noisy-channel communication theorem is obtained, along with some profound statements about the behavior of quantum information during generalised quantum measurements. The latter are very important in studies of quantum entanglement, but also in exploring the connections between thermodynamics, information theory, and quantum physics. This chapter also discusses equalities and inequalities related to entropy, the Holevo bound, capacity of a bosonic channel, information gained through measurements, relative entropy and thermodynamics, entropy increase due to erasure, and Landauer's erasure and data compression.

Sep 28, 20064 citations

On General Quantum Mutual Entropy and Capacity

Noborn Watanabe

In communication processes, a channel has an activity to communicate information of input system to output system. The mutual entropy (information) denotes an amount of information transmitted correctly from the input system to the output system through a channel. The (semi‐classical) mutual entropies for classical input and quantum output were defined by several researchers. The fully quantum mutual entropy, which is called Ohya mutual entropy, for quantum input and output by using the relative entropy was defined by Ohya in 1983, and he extended it to general quantum systems by means of the relative entropy of Araki and Uhlmann. The capacity shows the ability of the information transmission of the channel, which is used as a measure for construction of channels. The fully quantum capacity is formulated by taking the supremum of Ohya mutual entropy with respect to a certain subset of the initial state space. One of the most important theorems in quantum communication theory is coding theorem. The quantum coding theorems are discussed by using the mutual entropy — type measures introduced in the studies of quantum information.In this paper, we compare with these mutual entropy‐type measures in order to obtain most suitable one for discussing the quantum coding theorem. We concretely calculate the quantum capacity for quantum channels.

AIP conference proceedingsJan 1, 20050 citations

A Simple Heuristic Derivation of Shannon’s Formula for a Communication Channel with Continuous Variables in the Quantum Case

Igor M. Arbekov, S. N. Molotkov, I. V. Sinil’shchikov

Abstract The aim of the paper is the derivation of formulas for the capacities of a classical–quantum communication channel with Gaussian noise, which are analogs of the classical capacities and arise in many problems of quantum information theory, on a simple, heuristic and physically intuitively clear level. The classical capacity of a classical communication channel with limited frequency band and Gaussian information states diverges as noise tends to zero. In a consistent quantum consideration, the divergence is removed, which is a consequence of the fundamental physical principle of indistinguishability of particles—bosons in information states.

Journal of Experimental and Theoretical PhysicsMar 1, 20210 citations

The union of physics and information

Igor Devetak, Anne Staples

A union of quantum mechanics, thermodynamics and information theory is presented. It is accomplished by reinterpreting the mathematical formalism of Everett’s many-worlds theory of quantum mechanics and augmenting it to include preparation according to a given ensemble. The notion of directed entanglement is introduced through which both classical and quantum communication over quantum channels are reduced to entanglement transfer. The paradox of constant thermodynamic entropy in a closed quantum system is resolved. The view taken in this Letter is that the totality of conceptual experience can be described in terms of correlated random variables. This will allow us to make contact with Shannon’s information theory [1] in which random variables are the carriers of information. Two protagonists sharing the same physical world is no more than classical correlations between the states of their knowledge regarding that world. Similarly, the observation of definite physical laws is no more than classical correlations between states of knowledge regarding two consecutive acts of measurement, or preparation and measurement, depending on the experiment. For instance, a ball kicked by Alice seen as obeying Newton’s deterministic laws of motion is merely a statement about the correlation

Jan 1, 20021 citation