Related papers: A Generalized Statistical Complexity Measure: Appl…
Measuring the concentration of random variables is a fundamental concept in probability and statistics. Here, we explore a type of concentration measure for continuous random variables with bounded support and use it to provide a notion of…
The Renyi entropies constitute a family of information measures that generalizes the well-known Shannon entropy, inheriting many of its properties. They appear in the form of unconditional and conditional entropies, relative entropies or…
We present a complexity reduction algorithm for a family of parameter-dependent linear systems when the system parameters belong to a compact semi-algebraic set. This algorithm potentially describes the underlying dynamical system with…
The R{\'e}nyi entropy is one of the important information measures that generalizes Shannon's entropy. The quantum R{\'e}nyi entropy has a fundamental role in quantum information theory, therefore, bounding this quantity is of vital…
In this note a new method for computing the entanglement entropy of a CFT holographically is explored. It consists of finding a bulk background with a boundary metric that has the conical singularities needed to compute the entanglement…
A powerful tool is developed for the characterization of chaotic signals. The approach is based on the symbolic encoding of time series (according to their ordinal patterns) combined with the ensuing characterization of the corresponding…
We investigate the role of a statistical complexity measure to assign equilibration in isolated quantum systems. While unitary dynamics preserve global purity, expectation values of observables often exhibit equilibration-like behavior,…
We study a generic and paradigmatic two degrees of freedom system consisting of two coupled perturbed cat maps with different types of dynamics. The Wigner separability entropy (WSE) -- equivalent to the operator space entanglement entropy…
Statistical query (SQ) algorithms are algorithms that have access to an {\em SQ oracle} for the input distribution $D$ instead of i.i.d.~ samples from $D$. Given a query function $\phi:X \rightarrow [-1,1]$, the oracle returns an estimate…
We conduct a numerical investigation of the dynamics of the central spin model in the presence of measurement processes. This model holds promise for experimental exploration due to its topology, which facilitates the natural distinction of…
We explore a large class of correlation measures called the $\alpha-z$ R\'enyi mutual informations (RMIs). Unlike the commonly used notion of RMI involving linear combinations of R\'enyi entropies, the $\alpha-z$ RMIs are positive…
The generalized density matrix (GDM) method is used to calculate microscopically the parameters of the collective Hamiltonian. Higher order anharmonicities are obtained consistently with the lowest order results, the mean field…
We describe in detail the theory underpinning the measurement of density matrices of a pair of quantum two-level systems (``qubits''). Our particular emphasis is on qubits realized by the two polarization degrees of freedom of a pair of…
We will give a new model for measurements of a quantum system such that the measuring apparatuses are described by a unital separable non-type I nuclear simple C$^*$-algebra equipped with certain unital endomorphisms and pure states. An…
We apply a probabilistic approach to study the computational complexity of analog computers which solve linear programming problems. We analyze numerically various ensembles of linear programming problems and obtain, for each of these…
We consider Gibbs distributions, which are families of probability distributions over a discrete space $\Omega$ with probability mass function of the form $\mu^\Omega_\beta(\omega) \propto e^{\beta H(\omega)}$ for $\beta$ in an interval…
Quantum Hamiltonian complexity studies computational complexity aspects of local Hamiltonians and ground states; these questions can be viewed as generalizations of classical computational complexity problems related to local constraint…
The Shannon entropy, the desequilibrium and their generalizations (R\'enyi and Tsallis entropies) of the three-dimensional single-particle systems in a spherically-symmetric potential $V(r)$ can be decomposed into angular and radial parts.…
We consider the classical $k$-means clustering problem in the setting bi-criteria approximation, in which an algoithm is allowed to output $\beta k > k$ clusters, and must produce a clustering with cost at most $\alpha$ times the to the…
The internal disorder of hydrogenic Rydberg atoms as contained in their position and momentum probability densities is examined by means of the following information-theoretic spreading quantities: the radial and logarithmic expectation…