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Heisenberg's uncertainty principle and recently derived many no-go theorems including the no-cloning theorem and the no-deleting theorem have corroborated the idea that we can never access quantum information without causing disturbance.…

Quantum Physics · Physics 2008-04-16 Koji Azuma , Masato Koashi , Nobuyuki Imoto

The use of algorithmic information theory (Kolmogorov complexity theory) to explain the relation between mathematical probability theory and `real world' is discussed.

History and Overview · Mathematics 2015-05-13 Alexander Shen

This work presents a study of Kolmogorov complexity for general quantum states from the perspective of deterministic-control quantum Turing Machines (dcq-TM). We extend the dcq-TM model to incorporate mixed state inputs and outputs, and…

Quantum Physics · Physics 2024-01-24 Mariano Lemus , Ricardo Faleiro , Paulo Mateus , Nikola Paunković , André Souto

We derive the amount of information retrieved by a quantum measurement in estimating an unknown maximally entangled state, along with the pertaining disturbance on the state itself. The optimal tradeoff between information and disturbance…

Quantum Physics · Physics 2007-05-23 Massimiliano F. Sacchi

In this study, the effect of bounded quantum memory in a primitive information protocol has been examined using the quantum Kolmogorov complexity as a measure of information. We employed a toy two-party protocol in which Bob by using a…

Quantum Physics · Physics 2011-04-15 Takayuki Miyadera

We develop a theory of the algorithmic information in bits contained in an individual pure quantum state. This extends classical Kolmogorov complexity to the quantum domain retaining classical descriptions. Quantum Kolmogorov complexity…

Quantum Physics · Physics 2016-11-17 Paul M. B. Vitanyi

The quantum gravity has great difficulties with application of the probability notion. In given article this problem is analyzed according to algorithmic viewpoint. According to A.N. Kolmogorov, the probability notion can be connected with…

General Relativity and Quantum Cosmology · Physics 2009-10-28 V. D. Dzhunushaliev

When we extract information from a system by performing a quantum measurement, the state of the system is disturbed due to the backaction of the measurement. Numerous studies have been performed to quantitatively formulate tradeoff…

Quantum Physics · Physics 2016-04-06 Tomohiro Shitara , Yui Kuramochi , Masahito Ueda

We survey the diverse approaches to the notion of information content: from Shannon entropy to Kolmogorov complexity. The main applications of Kolmogorov complexity are presented namely, the mathematical notion of randomness (which goes…

Logic · Mathematics 2008-01-03 Marie Ferbus-Zanda , Serge Grigorieff

We survey the Kolmogorov's approach to the notion of randomness through the Kolmogorov complexity theory. The original motivation of Kolmogorov was to give up a quantitative definition of information. In this theory, an object is randomness…

Logic · Mathematics 2008-01-03 Marie Ferbus-Zanda , Serge Grigorieff

We consider separating the problem of designing Hamiltonian quantum feedback control algorithms into a measurement (estimation) strategy and a feedback (control) strategy, and consider optimizing desirable properties of each under the…

Quantum Physics · Physics 2009-11-06 Andrew C. Doherty , Kurt Jacobs , Gerard Jungman

In this paper, we present some results on information, complexity and entropy as defined below and we discuss their relations with the Kolmogorov-Sinai entropy which is the most important invariant of a dynamical system. These results have…

Dynamical Systems · Mathematics 2019-08-17 Vieri Benci , Claudio Bonanno , Stefano Galatolo , Giulia Menconi , Federico Ponchio

We survey diverse approaches to the notion of information: from Shannon entropy to Kolmogorov complexity. Two of the main applications of Kolmogorov complexity are presented: randomness and classification. The survey is divided in two parts…

Logic in Computer Science · Computer Science 2010-10-20 Marie Ferbus-Zanda , Serge Grigorieff

The word "complexity" is most often used as a meta--linguistic expression referring to certain intuitive characteristics of a natural system and/or its scientific description. These characteristics may include: sheer amount of data that…

History and Overview · Mathematics 2013-01-03 Yuri I. Manin

Information-theoretic definitions for the noise associated with a quantum measurement and the corresponding disturbance to the state of the system have recently been introduced [F. Buscemi et al., Phys. Rev. Lett. 112, 050401 (2014)]. These…

Quantum Physics · Physics 2016-12-14 Alastair A. Abbott , Cyril Branciard

We present a simple information-disturbance tradeoff relation valid for any general measurement apparatus: The disturbance between input and output states is lower bounded by the information the apparatus provides in distinguishing these…

Quantum Physics · Physics 2009-11-11 Lorenzo Maccone

When an observer wants to identify a quantum state, which is known to be one of a given set of non-orthogonal states, the act of observation causes a disturbance to that state. We investigate the tradeoff between the information gain and…

Quantum Physics · Physics 2009-10-28 Christopher A. Fuchs , Asher Peres

We compare the elementary theories of Shannon information and Kolmogorov complexity, the extent to which they have a common purpose, and where they are fundamentally different. We discuss and relate the basic notions of both theories:…

Information Theory · Computer Science 2020-07-21 Peter Grunwald , Paul Vitanyi

I consider the tradeoff between the information gained about an initially unknown quantum state, and the disturbance caused to that state by the measurement process. I show that for any distribution of initial states, the…

Quantum Physics · Physics 2007-05-23 Howard Barnum

The notions of error and disturbance appearing in quantum uncertainty relations are often quantified by the discrepancy of a physical quantity from its ideal value. However, these real and ideal values are not the outcomes of simultaneous…

Quantum Physics · Physics 2017-07-26 Joseph M. Renes , Volkher B. Scholz , Stefan Huber