相关论文: Quantum Kolmogorov Complexity

While Kolmogorov complexity is the accepted absolute measure of information content of an individual finite object, a similarly absolute notion is needed for the relation between an individual data sample and an individual model summarizing…

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…

We show that the mutual information, in the sense of Kolmogorov complexity, of any pair of strings $x$ and $y$ is equal, up to logarithmic precision, to the length of the longest shared secret key that two parties, one having $x$ and the…

A practical measure for the complexity of sequences of symbols (``strings'') is introduced that is rooted in automata theory but avoids the problems of Kolmogorov-Chaitin complexity. This physical complexity can be estimated for ensembles…

The information in an individual finite object (like a binary string) is commonly measured by its Kolmogorov complexity. One can divide that information into two parts: the information accounting for the useful regularity present in the…

Quantum systems are the ultimate touchstone for the production of random sequences of numbers. Spatially spread entangled systems allow the generation of identical random sequences in remote locations. The impossibility of observing a…

We discuss the Bennett-Brassard 1984 (BB84) quantum key distribution protocol in the light of quantum algorithmic information. While Shannon's information theory needs a probability to define a notion of information, algorithmic information…

We shed new light on entanglement measures in multipartite quantum systems by taking a computational-complexity approach toward quantifying quantum entanglement with two familiar notions--approximability and distinguishability. Built upon…

It is impossible to effectively modify a string in order to increase its Kolmogorov complexity. But is it possible to construct a few strings, not longer than the input string, so that most of them have larger complexity? We show that the…

Symmetry of information states that $C(x) + C(y|x) = C(x,y) + O(\log C(x))$. We show that a similar relation for online Kolmogorov complexity does not hold. Let the even (online Kolmogorov) complexity of an n-bitstring $x_1x_2... x_n$ be…

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…

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…

Kolmogorov complexity of a finite binary word reflects both algorithmic structure and the empirical distribution of symbols appearing in the word. Words with symbol frequencies far from one half have smaller combinatorial richness and…

There is no single definition of complexity (Edmonds 1999; Gershenson 2008; Mitchell 2009; De Domenico, et al., 2019), as it acquires different meanings in different contexts. A general notion is the amount of information required to…

Depth of an object concerns a tradeoff between computation time and excess of program length over the shortest program length required to obtain the object. It gives an unconditional lower bound on the computation time from a given program…

Kolmogorov-Chaitin complexity has long been believed to be impossible to approximate when it comes to short sequences (e.g. of length 5-50). However, with the newly developed \emph{coding theorem method} the complexity of strings of length…

For any quantum algorithm given by a path in the space of unitary operators we define the computational complexity as the typical computational time associated with the path. This time is defined using a quantum time estimator associated…

Randomness extraction is the process of constructing a source of randomness of high quality from one or several sources of randomness of lower quality. The problem can be modeled using probability distributions and min-entropy to measure…

Two-party one-way quantum communication has been extensively studied in the recent literature. We target the size of minimal information that is necessary for a feasible party to finish a given combinatorial task, such as distinction of…

We initiate a study of the complexity of quantum field theories (QFTs) by proposing a measure of information contained in a QFT and its observables. We show that from minimal assertions, one is naturally led to measure complexity by two…