Related papers: Free Entropy
Various limit-free formulas are given for the computation of the algebraic and the topological entropy, respectively in the settings of endomorphisms of locally finite discrete groups and of continuous endomorphisms of totally disconnected…
We define correlational (von Neumann) entropy for an individual quantum state of a system whose time-independent hamiltonian contains random parameters and is treated as a member of a statistical ensemble. This entropy is representation…
We give a complete answer to the questions of factoriality, type classification and fullness for arbitrary free product von Neumann algebras.
We give a closed-form solution of von Neumann entropy as a function of geometric phase modulated by visibility and average distinguishability in Hilbert spaces of two and three dimensions. We show that the same type of dependence also…
In this paper we study multi-matrix models whose potentials are perturbations of the quadratic potential associated with independent GUE random matrices. More precisely, we compute the free energy and the expectation of the trace of…
This paper revisits standard calculations of free field entanglement entropy in light of the newly developed lattice-continuum correspondence. This correspondence prescribes an explicit method to extract an approximately continuum quantum…
Several techniques together with some partial answers are given to the questions of factoriality, type classification and fullness for amalgamated free product von Neumann algebras.
We normalize the combinatorial Laplacian of a graph by the degree sum, look at its eigenvalues as a probability distribution and then study its Shannon entropy. Equivalently, we represent a graph with a quantum mechanical state and study…
We review the plethora of uncertainty relations that appear in quantum mechanics and their nuances. We present both foundational applications, e.g. in understanding and defining complementarity, and practical applications, e.g. in quantum…
Free probability provides a framework for describing correlations between non-commuting observables in complex quantum systems whose Hilbert-space states follow maximum-entropy distributions. We examine the robustness of this framework…
We introduce the notion of topological entropy of a formal languages as the topological entropy of the minimal topological automaton accepting it. Using a characterization of this notion in terms of approximations of the Myhill-Nerode…
Quantum physics, despite its observables being intrinsically of a probabilistic nature, does not have a quantum entropy assigned to them. We propose a quantum entropy that quantify the randomness of a pure quantum state via a conjugate pair…
In this paper, we show how the entropy (including the von Neumann entropy obtained by tracing across various sizes of subsystems, the entanglement gap, as well as different degrees of R\'{e}nyi entropy) of the random reduced density…
A large class of strongly correlated quantum systems can be described in certain large-N limits by quadratic in field actions along with self-consistency equations that determine the two-point functions. We use the replica approach and the…
The fermionic von Neumann entropy, the fermionic entanglement entropy and the fermionic relative entropy are defined for causal fermion systems. Our definition makes use of entropy formulas for quasi-free fermionic states in terms of the…
We introduce the concept of inflation word entropy for random substitutions with a constant and primitive substitution matrix. Previous calculations of the topological entropy of such systems implicitly used this concept and established…
Suppose X is an n-tuple of selfadjoint elements in a tracial von Neumann algebra M. If z is a selfadjoint element in M and for some selfadjoint element y in the von Neumann algebra generated by X $\delta_0(y, z) < \delta_0(y) +…
We apply a common measure of randomness, the entropy, in the context of iterated functions on a finite set with n elements. For a permutation, it turns out that this entropy is asymptotically (for a growing number of iterations) close to…
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 general relation between entropy and an evolutionary superoperator is derived based on the theory of the real-time formulation. The formulation establishing the relation relies only on the framework of quantum statistical mechanics and…