Mathematical models are an essential component of quantitative science. They generate
predictions about the future, based on information available in the present. In the spirit of …

We derive quantum counterparts of two key theorems of classical information theory,
namely, the rate-distortion theorem and the source-channel separation theorem. The rate …

Quantum data compression is of great significance to both quantum computation and
quantum communication due to the limited resources for quantum storage. Here in this …

We show that there exists a universal quantum Turing machine (UQTM) that can simulate
every other QTM until the other QTM has halted and then halt itself with probability one. This …

We simply construct a quantum universal variable-length source code in which, independent
of information source, both of the average error and the probability that the coding rate is …

The purpose of this thesis is to give a formal definition of quantum Kolmogorov complexity
(QC), and rigorous mathematical proofs of its basic properties. The definition used here is …

We have proven that there exists a quantum state approximating any multi-copy state
universally when we measure the error by means of the normalized relative entropy. While …

Based on the problem of quantum data compression in a lossless way, we present here an
operational interpretation for the family of quantum Rényi entropies. In order to do this, we …

The Kolmogorov complexity of a string is the minimum length of a programme that can
produce that string. Information distance between two strings based on Kolmogorov …

The Kolmogorov complexity of a string is the length of its shortest description. We define a
second quantized Kolmogorov complexity where the length of a description is defined to be …