Related papers: Introduction to Quantum Message Space
The field of Information Theory is founded on Claude Shannon's seminal ideas relating to entropy. Nevertheless, his well-known avoidance of meaning (Shannon, 1948) still persists to this day, so that Information Theory remains poorly…
The notion of Shannon entropy is crucial for the theory of classical information. In quantum information theory, an analogous key role is played by the von Neumann entropy: quantum information processing is closely related to entropy…
Quantum Theory is one of the pillars of modern science developed over the last hundred years. In this review paper we introduce, step by step, the quantum theory understood as a mathematical model describing quantum experiments. We start…
We give a review of concepts related to connection of classical and quantum theories, from the phase space perspective. Quantum theory is described by non-commutative operators of coordinates and momenta, results in values having a certain…
Quantum applications transmit and receive data through quantum and classical communication channels. Channel capacity, the distance and the photon path between transmitting and receiving parties and the speed of the computation links play…
This is a self-contained review on the theory of quantum group and its applications to modern physics. A brief introduction is given to the Yang-Baxter equation in integrable quantum field theory and lattice statistical physics. The quantum…
The entanglement-assisted classical capacity of a quantum channel is known to provide the formal quantum generalization of Shannon's classical channel capacity theorem, in the sense that it admits a single-letter characterization in terms…
We propose in this note the study of quantum channels from association schemes. This is done by interpreting the $(0,1)$-matrices of a scheme as the Kraus operators of a channel. Working in the framework of one-shot zero-error information…
Quantum computing improves substantially on known classical algorithms for various important problems, but the nature of the relationship between quantum and classical computing is not yet fully understood. This relationship can be…
In the first part of this thesis, we discuss the algebraic approach to classical and quantum physics and develop information theoretic concepts within this setup. In the second part, we discuss the uncertainty principle in quantum…
The influence of additional information on the decision making of agents, who are interacting members of a society, is analyzed within the mathematical framework based on the use of quantum probabilities. The introduction of social…
An upper limit is given to the amount of quantum information that can be transmitted reliably down a noisy, decoherent quantum channel. A class of quantum error-correcting codes is presented that allow the information transmitted to attain…
We consider quantum channels with two senders and one receiver. For an arbitrary such channel, we give multi-letter characterizations of two different two-dimensional capacity regions. The first region is comprised of the rates at which it…
A class of quantum analogues of compact symmetric spaces of classical type is introduced by means of constant solutions to the reflection equations. Their zonal spherical functions are discussed in connection with $q$-orthogonal…
Shannon's mathematical theory of communication defines fundamental limits on how much information can be transmitted between the different components of any man-made or biological system. This paper is an informal but rigorous introduction…
Information theory establishes the ultimate limits on performance for noisy communication systems [Shannon48]. An accurate model of a physical communication device must include quantum effects, but typically including these makes the theory…
We propose a model of communication employing two harmonic oscillator detectors interacting through a scalar field in a background Minkowski spacetime. In this way, the scalar field plays the role of a quantum channel, namely a Bosonic…
We present two approaches for transmitting classical information over quantum broadcast channels. The first technique is a quantum generalization of the superposition coding scheme for the classical broadcast channel. We use a quantum…
The work is devoted to study of quantum mutual information and coherent information -- the two important characteristics of quantum communication channel. Appropriate definitions of these quantities in the infinite-dimensional case are…
This is a short, self-contained expository survey, focused on algebraic and analytic aspects of quantum groups. Topics covered include the definition of ``quantum group,'' the Yang-Baxter equation, quantized universal enveloping algebras,…