Dai Fangwen,Ma Lei.Calculation of entanglement entropy for continuous-variable entangled state based on general two-mode Boson exponential quadratic operator in Fock space. Communications in Theoretical Physics . 2008Dai Fangwen,Ma Lei. Calculation of entanglement entropy for continuous-variable entangled...
It made use of the characteristics of the information content(entropy) of a continuous variable, and partitioned the continuous variable by itself for minimizing both the loss of entropy and the number of partitions, in order to find the best balance between the information loss and a low ...
The definition of Rényi entropy can be extended to continuous random variables by but unlike the discrete case, Rényi entropy can be negative for continuous random variables, and so Rényi entropy is typically only used for discrete variables. For example, letXbe the random variable defined on ...
Use will be made of the condition for a continuous function to be invertible, namely that its derivative must be finite and nonzero on the interior of its domain. Energy–Entropy Because the entropy is continuous and strictly concave, S″ < 0, it can have at most one turning point. ...
For classical systems, the discrete index i is replaced by a real continuous variable x, and we have the form that was used by Boltzmann and Gibbs themselves, namely 𝑆𝐵𝐺≡−𝑘∫𝑑𝑥𝑝(𝑥)ln𝑝(𝑥)(∫𝑑𝑥𝑝(𝑥)=1). (2) (Some mathematical care might be ...
(Renyi1951) have been receiving much attention in recent years. Another popular formulation of entropy is the cross-entropy or relative entropy due to Kullback and Leibler (1951) which is a generalization of the Shannon entropy. For a continuous random variableXwith a probability density function ...
内容提示: Acta Mathematica Scientia 2012,32B(2):775–782http://actams.wipm.ac.cnENTROPY FUNCTIONAL FOR CONTINUOUSSYSTEMS OF FINITE ENTROPY∗M. RahimiA. RiaziDepartment of Mathematics, Amirkabir University of Technology, Tehran, IranE-mail: mr rahimi@aut.ac.ir; Riazi@aut.ac.irAbstractIn this...
For discrete- and continuous-variable QKD, for example, one can use the entropic uncertainty relations32,33. When dealing with DIQKD, a quantum advantage in a Bell game implies a lower-bound on \(H\left( {K_i\left| {E_i} \right.} \right)\) as discussed above....
Proof For a continuous decreasing function f we have b a f (m)dm ≤ f (a) + b a f (m)dm. Moreover, b m=a f (m) ≤ n log n dm m logα−1 m = (ln 2)d p pα−1 = ln 2 2−α log2−α n − 1 , α∈ (1, 2), (ln2 2) log log n, α = 2, ...
An entropy formula for the heat equation on manifolds with time-dependent metric, application to ancient solutions - Guo, Philipowski, et al. () Citation Context ...iable and continuous in the second variable. This time-dependent stochastic differential equation has intrinsic links to non-linear...