QUANTUM ENTROPY, INFORMATION AND COMMUNICATIONS
Quantum Relative Entropy (QRE)
traces back to work of von Neumann in the early 30s
on mathematical foundations of quantum theory and his definition
of quantum entropy. The new development started in the mid of 60s
when by R L Stratonovich introduced the mutual quantum entropy for two coupled systems
and found the entropy bound for the capacity of the quantum Gaussian channel.
It has taken off worldwide particularly in the last
fifteen years due to the prospects of quantum communications and computations.
Some simple quantum algorithms have been recently demonstrated experimentally,
and possible realizations of quantum computer have been proposed.
New theoretical possibilities have been opened recently in the result
of the discovery of a new, truly quantum entropy
and entangled quantum information. These are planned to develop in this project
with the aim of extending the dynamical entropy bounds
into the domain of quantum stochastics for information dynamics.
Quantum Information and Communications (QIC)
is a mathematical framework for study of communications
in quantum channels and the processes of decrease of quantum entropy
and uncertainties via encodings and quantum measurements.
It consists of quantum bits (qubits). The qubit
is the basic unit of quantum information
representing a choice from infinitely many equally possible quantum states
of a two-level atom or any other quantum bit
such as quantum spin 1/2 or photon polarization.
It is not a part of classical information theory
but a noncommutative generalization of it which is necessary,
and hopefully will be sufficient to study the potential capabilities
of quantum information.
My 10 Relevant Publications:
- V. P. Belavkin and B. Grishanin:
An Optimal Quantisation of Random Vectors.
Rep. of USSR Academy of Sciences, Tech. Cybernetics
1 161--169 (1970).
- V. P. Belavkin:
Optimal Adaptive Quantisation.
Rep. of USSR Academy of Sciences, Tech. Cybernetics
4 164--171 (1971).
- V. P. Belavkin and R. Stratonovich:
On Optimisation of Processing of Quantum Signals by Information Criterion.
Radio Eng Electron Physics 18 (9) 1839--1844 (1973).
quant-ph/0511042,
PDF.
- V. P. Belavkin:
Optimal Linear Random Filtration of Quantum Boson Signals.
Problems of Control and Information Theory 3 (4) 47--62 (1974).
- V. P. Belavkin and A. Vantsian:
On Sufficient Conditions of Optimality of Quantum Signal Processing.
Radio Eng Electron Physics
19 (7) 1391--1395 (1974).
quant-ph/0511043,
PDF.
- V. P. Belavkin and P. Staszewski:
Conditional Entropy and Entropy in Quantum Statistics.
Annals de l'insitut Henri Poincare: Phys Theor
37 51--57 (1982).
- V. P. Belavkin and P. Staszewski:
Relative Entropy in C*-Algebraic Statistical Mechanics.
Reports on Mathematical Physics
20 373--384 (1984).
- V. P. Belavkin & P. Staszewski:
A Radon-Nikodym Theorem for Completely Positive Maps.
Reports on Mathematical Physics
24 (1) 49--55 (1986).
quant-ph/06...,
PDF.
- V. P. Belavkin:
Towards Quantum epsilon-Entropy and Validity of Quantum Information.
Maximum Entropy and Bayesian Methods 163--165.
Kluwer Publisher, 1993.
- V. P. Belavkin and M. Ohya:
Quantum Entropy and Information in Discrete Entangled States.
Inf Dim Anal, Quant Prob & Rel Topics (2001) 4 No. 2, 137-160.
quant-ph/0004069,
PDF.