Related papers: Min- and Max-Entropy in Infinite Dimensions

We carry out a systematic study of entanglement entropy in nonrelativistic conformal field theories via holographic techniques. After a discussion of recent results concerning Galilean conformal field theories, we deduce a novel expression…

We develop a rigorous framework for quantifying quantum coherence in finite-dimensional systems by applying the Schur-Horn majorization theorem to relate eigenvalue distributions and diagonal entries of density matrices. Building on this…

In this paper, we introduce two bounds which we call the Upper Differential Entropy and the Lower Differential Entropy for an infinite family of intervals(strips) in quantum field theory. The two bounds are equal provided that the theory is…

We study local asymptotic normality of M-estimates of convex minimization in an infinite dimensional parameter space. The objective function of M-estimates is not necessary differentiable and is possibly subject to convex constraints. In…

Ill-posed inverse problems of the form y = X p where y is J-dimensional vector of a data, p is m-dimensional probability vector which cannot be measured directly and matrix X of observable variables is a known J,m matrix, J < m, are…

Within an inherently classical perspective, there is always an unavoidable energy cost associated with the information deletion and this common lore is at the heart of the Landauer's conjecture that does not impose, per se, any relevant…

Motivated by the apparent lack of a workable hypothesis we developed a model to describe phenomena such as entanglement and the EPR-paradox. In the model we propose the existence of extra hidden dimensions. Through these dimensions it will…

The paper search for the minimum of the entropy of a two- dimensional distribution in the Fr\'echet class, the class of distributions with given marginals. The main result for discrete distributions is an algorithm for building the…

The principle of maximum entropy provides a useful method for inferring statistical mechanics models from observations in correlated systems, and is widely used in a variety of fields where accurate data are available. While the assumptions…

Entanglement entropy in topologically ordered matter phases has been computed extensively using various methods. In this paper, we study the entanglement entropy of topological phases in two-spaces from a new perspective---the perspective…

As an alternative to the well-known methods of "chaining" and "bracketing" that have been developed in the study of random fields, a new method, which is based on a stochastic maximal inequality derived by using the Taylor expansion, is…

The relaxed maximum entropy problem is concerned with finding a probability distribution on a finite set that minimizes the relative entropy to a given prior distribution, while satisfying relaxed max-norm constraints with respect to a…

Formalising the confrontation of opinions (models) to observations (data) is the task of Inferential Statistics. Information Theory provides us with a basic functional, the relative entropy (or Kullback-Leibler divergence), an asymmetrical…

Within the task of collaborative filtering two challenges for computing conditional probabilities exist. First, the amount of training data available is typically sparse with respect to the size of the domain. Thus, support for higher-order…

In the framework of quasi-Hermitian quantum mechanics it is shown that a weakening of the isotropy of the Hilbert-space geometry can help us to enlarge the domain of the parameters at which the evolution is unitary. The idea is tested using…

In this paper, we study asymptotic expansion at infinity and symmetry of zero mean curvature equations of gradient graph in dimension 2, which include the Monge--Amp\`ere equation, inverse harmonic Hessian equation and the special…

The ability of many powerful machine learning algorithms to deal with large data sets without compromise is often hampered by computationally expensive linear algebra tasks, of which calculating the log determinant is a canonical example.…

We use a mix of field theoretic and holographic techniques to elucidate various properties of quantum entanglement entropy. In (3+1)-dimensional conformal field theory we study the divergent terms in the entropy when the entangling surface…

The restrictions that nature places on the distribution of correlations in a multipartite quantum system play fundamental roles in the evolution of such systems, and yield vital insights into the design of protocols for the quantum control…

How to find unknown distributions is questioned in many pieces of research. There are several ways to figure them out, but the main question is which acts more reasonably than others. In this paper, we focus on the maximum entropy principle…