相关论文: Entropy and Quantum Kolmogorov Complexity: A Quant…

Given the algebra of observables of a quantum system subject to selection rules, a state can be represented by different density matrices. As a result, different von Neumann entropies can be associated with the same state. Motivated by a…

We consider free fermion systems in arbitrary dimensions and represent the occupation pattern of each eigenstate as a classical binary string. We find that the Kolmogorov complexity of the string correctly captures the scaling behavior of…

B. Schumacher and M. Westmoreland have established a quantum analog of a well-known classical information theory result on a role of relative entropy as a measure of non-optimality in (classical) data compression. In this paper, we provide…

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…

We discuss information-theoretic concepts on infinite-dimensional quantum systems. In particular, we lift the smooth entropy formalism as introduced by Renner and collaborators for finite-dimensional systems to von Neumann algebras. For the…

A model of a quantum information source is proposed, based on the Gibbs ensemble of ideal (free) particles (bosons or fermions). We identify the (thermodynamic) von Neumann entropy as the information rate and establish the classical…

A unified combinatorial definition of the information content and entropy of different types of patterns, compatible with the traditional concepts of information and entropy, going beyond the limitations of Shannon information interpretable…

In a recent paper Andrei N. Soklakov explained the foundations of the Lagrangian formulation of classical particle mechanics by means of Kolmogorov complexity. In the present paper we use some of Soklakov ideas in order to derive the second…

In this Thesis, several results in quantum information theory are collected, most of which use entropy as the main mathematical tool. *While a direct generalization of the Shannon entropy to density matrices, the von Neumann entropy behaves…

Quantum mechanics and information theory are among the most important scientific discoveries of the last century. Although these two areas initially developed separately it has emerged that they are in fact intimately related. In this…

Integral representations of quantum relative entropy, and of the directional second and higher order derivatives of von Neumann entropy, are established, and used to give simple proofs of fundamental, known data processing inequalities: the…

We describe an alternative method (to compression) that combines several theoretical and experimental results to numerically approximate the algorithmic (Kolmogorov-Chaitin) complexity of all $\sum_{n=1}^82^n$ bit strings up to 8 bits long,…

We extend the data compression theorem to the case of ergodic quantum information sources. Moreover, we provide an asymptotically optimal compression scheme which is based on the concept of high probability subspaces. The rate of this…

A new axiomatic characterization with a minimum of conditions for entropy as a function on the set of states in quantum mechanics is presented. Traditionally unspoken assumptions are unveiled and replaced by proven consequences of the…

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…

Many of the traditional results in information theory, such as the channel coding theorem or the source coding theorem, are restricted to scenarios where the underlying resources are independent and identically distributed (i.i.d.) over a…

The Kolmogorov complexity of x, denoted C(x), is the length of the shortest program that generates x. For such a simple definition, Kolmogorov complexity has a rich and deep theory, as well as applications to a wide variety of topics…

This work is originally a Cambridge Part III essay paper. Quantum complexity arises as an alternative measure to the Fubini metric between two quantum states. Given two states and a set of allowed gates, it is defined as the least complex…

Quantum machine learning (QML) holds promise for accelerating pattern recognition, optimization, and data analysis, but the conditions under which it can truly outperform classical approaches remain unclear. Existing research often…

Characterizing complexity and criticality in quantum systems requires diagnostics that are both computationally tractable and physically insightful. We apply a measure of quantum state complexity for n-qubit systems, defined as the…