Related papers: Quantum Kolmogorov Complexity and Information-Dist…
It has been shown that Information-Disturbance theorem can play an important role in security proof of quantum cryptography. The theorem is by itself interesting since it can be regarded as an information theoretic version of uncertainty…
In classical information theory, entropy rate and Kolmogorov complexity per symbol are related by a theorem of Brudno. In this paper, we prove a quantum version of this theorem, connecting the von Neumann entropy rate and two notions of…
The engine that powers quantum cryptography is the principle that there are no physical means for gathering information about the identity of a quantum system's state (when it is known to be prepared in one of a set of nonorthogonal states)…
In analogy of classical Kolmogorov complexity we develop a theory of the algorithmic information in bits contained in any one of continuously many pure quantum states: quantum Kolmogorov complexity. Classical Kolmogorov complexity coincides…
In 1927, Heisenberg heuristically disclosed the tradeoff between the error in the measurement and the caused disturbance on another complementary observable. In the quantum theory, most of uncertainty relations are proposed to reveal the…
I discuss several aspects of information theory and its relationship to physics and neuroscience. The unifying thread of this somewhat chaotic essay is the concept of Kolmogorov or algorithmic complexity (Kolmogorov Complexity, for short).…
We show that the global balance of information dynamics for general quantum measurements given in [F. Buscemi, M. Hayashi, and M. Horodecki, Phys.Rev.Lett. 100, 210504 (2008)] makes it possible to unify various and generally inequivalent…
In this paper we give a definition for quantum Kolmogorov complexity. In the classical setting, the Kolmogorov complexity of a string is the length of the shortest program that can produce this string as its output. It is a measure of the…
We introduce information-theoretic definitions for noise and disturbance in quantum measurements and prove a state-independent noise-disturbance tradeoff relation that these quantities have to satisfy in any conceivable setup. Contrary to…
The engine that powers quantum cryptography is the principle that there are no physical means for gathering information about the identity of a quantum system's state (when it is known to be prepared in one of a set of nonorthogonal states)…
We provide a general framework for quantifying the optimal tradeoff between the information retrieved by a quantum measurement and the disturbance on the quantum state in covariant quantum state estimation.
Common misconceptions on the Heisenberg principle are reviewed, and the original spirit of the principle is reestablished in terms of the trade-off between information retrieved by a measurement and disturbance on the measured system. After…
Algorithmic information theory studies description complexity and randomness and is now a well known field of theoretical computer science and mathematical logic. There are several textbooks and monographs devoted to this theory where one…
We introduce algorithmic information theory, also known as the theory of Kolmogorov complexity. We explain the main concepts of this quantitative approach to defining `information'. We discuss the extent to which Kolmogorov's and Shannon's…
Kolmogorov complexity is a measure of the information contained in a binary string. We investigate here the notion of quantum Kolmogorov complexity, a measure of the information required to describe a quantum state. We show that for any…
The measurement of an informative observable strongly disturbs a quantum state. We examine the so-called information-disturbance relation by introducing order relations based on the state distinction power of an observable and a variety of…
We address the problem of the information-disturbance trade-off associated to the estimation of a quantum transformation, and show how the extraction of information about the a black box causes a perturbation of the corresponding…
In this paper, we revisit a central concept in Kolmogorov complexity in which one would equate program-size complexity with information content. Despite the fact that Kolmogorov complexity has been widely accepted as an objective measure of…
Kolmogorov argued that the concept of information exists also in problems with no underlying stochastic model (as Shannon's information representation) for instance, the information contained in an algorithm or in the genome. He introduced…
We introduce a notion of Kolmogorov complexity of unitary transformation, which can (roughly) be understood as the least possible amount of information required to fully describe and reconstruct a given finite unitary transformation. In the…