Related papers: Entropy, Maximum Entropy Priciple and quantum stat…
We develop a martingale theory to describe fluctuations of entropy production for open quantum systems in nonequilbrium steady states. Using the formalism of quantum jump trajectories, we identify a decomposition of entropy production into…
Regularized quantum information metrics are calculated for the scattering process $e^-e^+ \rightarrow \gamma,Z\rightarrow \mu^-\mu^+$ that has a witness photon entangled with the initial electron-positron state. Unitarity implies the…
The study of generic properties of quantum states has led to an abundance of insightful results. A meaningful set of states that can be efficiently prepared in experiments are ground states of gapped local Hamiltonians, which are well…
A complex quantum system with energy dissipation is considered. The quantum Hamiltonians $H$ belong the complex Ginibre ensemble. The complex-valued eigenenergies $Z_{i}$ are random variables. The second differences $\Delta^{1} Z_{i}$ are…
Bayesian statistics in the frame of the maximum entropy concept has widely been used for inferential problems, particularly, to infer dynamic properties of strongly correlated fermion systems from Quantum-Monte-Carlo (QMC) imaginary time…
In this paper, we review the concept of entropy in connection with the description of quantum unstable systems. We revise the conventional definition of entropy due to Boltzmann and extend it so as to include the presence of complex-energy…
Maximum entropy inference and learning of graphical models are pivotal tasks in learning theory and optimization. This work extends algorithms for these problems, including generalized iterative scaling (GIS) and gradient descent (GD), to…
During a spontaneous change, a macroscopic physical system will evolve towards a macro-state with more realizations. This observation is at the basis of the Statistical Mechanical version of the Second Law of Thermodynamics, and it provides…
We derive an optimal bound on the sum of entropic uncertainties of two or more observables when they are sequentially measured on the same ensemble of systems. This optimal bound is shown to be greater than or equal to the bounds derived in…
Statistical mechanics relies on the complete though probabilistic description of a system in terms of all the microscopic variables. Its object is to derive therefrom static and dynamic properties involving some reduced set of variables.…
The variance of the number of particles in a set is an important quantity in understanding the statistics of non-interacting fermionic systems in low dimensions. An exact map of their ground state in a harmonic trap in one and two…
Mutual information I in infinite sequences (and in their finite prefixes) is essential in theoretical analysis of many situations. Yet its right definition has been elusive for a long time. I address it by generalizing Kolmogorov Complexity…
A system composed of identical spins and described by a quantum mechanical pure state is analyzed within the statistical framework presented in Part I of this work. We explicitly derive the typical values of the entropy, of the energy, and…
Many-body states that are invariant under particle relabelling, the permutation symmetric states, occur naturally when the system dynamics is described by symmetric processes or collective spin operators. We derive expressions for the…
An essential quantity in quantum information theory is the von Neumann entropy which depends entirely on the quantum density operator. Once known, the density operator reveals the statistics of observables in a quantum process, and the…
The minimum error entropy (MEE) criterion has been verified as a powerful approach for non-Gaussian signal processing and robust machine learning. However, the implementation of MEE on robust classification is rather a vacancy in the…
The electronic density \rho(r) in atoms, molecules and solids is, in general, a distribution that can be observed experimentally, containing spatial information projected from the total wave function. These density distributions can be…
Information plays an important role in our understanding of the physical world. We hence propose an entropic measure of information for any physical theory that admits systems, states and measurements. In the quantum and classical world,…
Three recently suggested random matrix ensembles (RME) are linked together by an exact mapping and plausible conjections. Since it is known that in one of these ensembles the eigenvector statistics is multifractal, we argue that all three…
We characterize information as risk reduction between knowledge states represented by partitions of the underlying probability space. Entropy corresponds to risk reduction from no (or partial) knowledge to full knowledge about a random…