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Fault tolerance and ultimate physical limits of nanocomputation
Published in David Crawley, Konstantin Nikolić, Michael Forshaw, 3D Nanoelectronic Computer Architecture and Implementation, 2020
A S Sadek, K Nikolić, M Forshaw
The quantum generalization of the probability distributions in information theory, p(x), are density matrices ρ [79]. In turn, the quantum generalization of the Shannon entropy, von Neumann entropy, can be constructed from these: H = −Trρ ln ρ. Just as classical information becomes entropy after interacting with a heat bath, quantum information decoheres after becoming entangled with the environment, maximizing the von Neumann entropy.
Texture and Quantum Entropy Algorithms for Oil Spill Detection in Synthetic Aperture Radar Images
Published in Maged Marghany, Automatic Detection Algorithms of Oil Spill in Radar Images, 2019
The von Neumann entropy is the analog of the Boltzmann entropy in quantum mechanics. Any density matrix ρ can be written as () ρ=∑ipi|i〉〈i|
Using relative von Neumann and Shannon entropies for feature fusion
Published in International Journal of Systems Science, 2019
Weimin Peng, Huifang Deng, Aihong Chen, Jing Chen
Based on the von Neumann entropy theory, the von Neumann entropy of the feature sample is defined as And the relative von Neumann entropy of the feature sample to the feature sample has the following definition (Vedral, 2002). For comparison, the computation model for relative Shannon entropy is also based on the relative entropy theory (Vedral, 2002), and is similar to the one for relative von Neumann entropy. As the computation model for von Neumann entropy is different to the one for Shannon entropy, there are some differences between the models for relative von Neumann and Shannon entropies. Given the probability of the feature sample , the Shannon entropy of the feature sample and the relative Shannon entropy of the feature sample to the feature sample are supposed to be defined as
Dynamics of a deformed atom cavity field system in presence of a Kerr-like medium
Published in Journal of Modern Optics, 2019
In this section, we are attempting to analyse the quantum correlation between a vee-type three-level atom and a single-mode coherent field by means of their entanglement. It is shown that, for any multipartite quantum system that is described by a pure state, the quantum entropy is a suitable measure to obtain the entanglement between the subsystems (49). According to Araki and Lieb (50), for a bipartite quantum system, the entropies of the system and subsystems (here atom and field) at any time t are limited by the triangle inequality , where S shows the total entropy of the system and the subscripts A and F refer to the atom and field, respectively. As a consequence of this inequality, if the system starts from a pure state (as we have considered the atom and the field are initially in a disentangled pure state), the total entropy of the system is zero and remains constant. That means at any time t>0, (51) and we only need to evaluate the reduced entropy of the atom/field to characterize the entanglement. According to the von Neumann entropy, the reduced field entropy is defined as where the reduced density matrix of the atom is given by and 's, j=1,2,3 are the eigenvalues of (16). Equation (15) essentially gives a measure of the degree of entanglement between the three-level V atom and the single-mode coherent field. If takes its minimum value zero, the field and the atom are disentangled. They are called maximally entangled if goes to 1.
The paradigm of complex probability and Ludwig Boltzmann's entropy
Published in Systems Science & Control Engineering, 2018
It is meaningful to assign a ‘joint entropy,’ because positions and momenta are quantum conjugate variables and are therefore not jointly observable. Mathematically, they have to be treated as joint distribution. Note that this joint entropy is not equivalent to the Von Neumann entropy, . Hirschman's entropy is said to account for the full information content of a mixture of quantum states.