In this work, a canonical method to compute entanglement entropy is proposed. We show that for two-dimensional conformal theories defined in torus, choice of moduli space allows the typical operator TFD provide degrees freedom segment and their complement. procedure, it not necessary make an analytic continuation from Rényi von Neumann calculated directly expected value operator. also propose m...

The subject is the overview of the use of quasi-entropy in finite dimensional spaces. Operator monotone functions and relative modular operators are used. The origin is the relative entropy, and the f -divergence, monotone metrics, covariance and the χ2-divergence are the most important particular cases. The extension of monotone metrics to those with two parameters is a new concept. Monotone m...

We study the fundamental properties of the quantum f -relative entropy, where f(·) is an operator convex function. We give the equality conditions under monotonicity and joint convexity, and these conditions are more general than, since they hold for a class of operator convex functions, and different for f(t) = − ln(t) from, the previously known conditions. The quantum f -entropy is defined in...

Minimization problems with respect to a one-parameter family of generalized relative entropies are studied. These relative entropies, which we term relative α-entropies (denoted Iα), arise as redundancies under mismatched compression when cumulants of compressed lengths are considered instead of expected compressed lengths. These parametric relative entropies are a generalization of the usual r...

 In this paper we study the relative entropy rate between a homogeneous Markov chain and a hidden Markov chain defined by observing the output of a discrete stochastic channel whose input is the finite state space homogeneous stationary Markov chain. For this purpose, we obtain the relative entropy between two finite subsequences of above mentioned chains with the help of the definition of...

In this paper, we have investigated the dependence of the spectral entanglement and indistinguishability of photon pairs produced by the spontaneous parametric down-conversion (SPDC) procedure on the bandwidth of spectral filters used in the detection setup. The SPDC is a three-wave mixing process which occurs in a nonlinear crystal and generates entangled photon pairs and utilizes as one of th...

We consider the general problem of relative entropy minimization and entropy maximization subject to expectation constraints. We show that the solutions can be represented as members of an exponential family subject to weaker conditions than previously shown, and the representation can be simplified further if an appropriate conjugate prior density is used. As a result, the solutions can be fou...

The subject of this work is the parametric inference problem, i.e. how to infer from data on the parameters of the data likelihood of a random process whose parametric form is known a priori. The assumption that Bayes’ theorem has to be used to add new data samples reduces the problem to the question of how to specify a prior before having seen any data. For this subproblem three theorems are s...

It is well known that for pure states the relative entropy of entanglement equal to reduced entropy, and closest separable state explicitly as well. The same holds Renyi per recent results. We ask question a quasi-relative entanglement, which an measure defined minimum distance set state, when measured by entropy. First, we consider maximally entangled show any entanglement. Then, this also cer...