相关论文: Maximum entropy principle and quantum statistical …
We construct a very general family of characteristic functions describing Random Matrix Ensembles (RME) having a global unitary invariance, and containing an arbitrary, one-variable probability measure which we characterize by a `spread…
The method of Maximum (relative) Entropy (ME) is used to translate the information contained in the known form of the likelihood into a prior distribution for Bayesian inference. The argument is guided by intuition gained from the…
The density matrix is a positive semidefinite operator of trace 1 characterizing the state of a quantum system. We consider the inverse problem to reconstruct such density matrices from indirect measurements, also known as quantum state…
Systems with long-range interactions display a short-time relaxation towards Quasi Stationary States (QSS) whose lifetime increases with the system size. In the paradigmatic Hamiltonian Mean-field Model (HMF) out-of-equilibrium phase…
Predicting the stationary behavior of observables in isolated many-body quantum systems is a central challenge in quantum statistical mechanics. While one can often use the Gibbs ensemble, which is simple to compute, there are many…
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…
A local and distributive algorithm is proposed to find an optimal trial wave-function minimizing the Hamiltonian expectation in a quantum system. To this end, the quantum state of the system is connected to the Gibbs state of a classical…
One of the most counterintuitive aspects of quantum theory is its claim that there is 'intrinsic' randomness in the physical world. Quantum information science has greatly progressed in the study of intrinsic, or secret, quantum randomness…
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…
To guarantee the security of uniform random numbers generated by a quantum random number generator, we study secure extraction of uniform random numbers when the environment of a given quantum state is controlled by the third party, the…
A one-parameter random matrix model is proposed for describing the statistics of the local amplitudes and phases of electron eigenfunctions in a mesoscopic quantum dot in an arbitrary magnetic field. Comparison of the statistics obtained…
Using random matrix techniques and the theory of Matrix Product States we show that reduced density matrices of quantum spin chains have generically maximum entropy.
The field of complex networks studies a wide variety of interacting systems by representing them as networks. To understand their properties and mutual relations, the randomisation of network connections is a commonly used tool. However,…
The study of quantum and classical correlations between subsystems is fundamental to understanding many-body physics. In quantum information theory, the quantum mutual information, $I(A;B)$, is a measure of correlation between the…
Knowing and guessing, these are two essential epistemological pillars in the theory of quantum-mechanical measurement. As formulated quantum mechanics is a statistical theory. In general, a priori unknown states can be completely determined…
Information-theoretic measures such as relative entropy and correlation are extremely useful when modeling or analyzing the interaction of probabilistic systems. We survey the quantum generalization of 5 such measures and point out some of…
Maximum entropy principle identifies forces conjugated to observables and the thermodynamic relations between them, independent upon their underlying mechanistic details. For data about state distributions or transition statistics, the…
We obtain exact analytic expressions for a class of functions expressed as integrals over the Haar measure of the unitary group in d dimensions. Based on these general mathematical results, we investigate generic dynamical properties of…
Multi-instance data, in which each object (bag) contains a collection of instances, are widespread in machine learning, computer vision, bioinformatics, signal processing, and social sciences. We present a maximum entropy (ME) framework for…
We consider the analysis of probability distributions through their associated covariance operators from reproducing kernel Hilbert spaces. We show that the von Neumann entropy and relative entropy of these operators are intimately related…