scholarly journals A Note on Complexities by Means of Quantum Compound Systems

Entropy ◽  
2020 ◽  
Vol 22 (3) ◽  
pp. 298
Author(s):  
Noboru Watanabe
Keyword(s):  
Information Transfer ◽  
Probability Distributions ◽  
Joint Probability ◽  
Quantum Systems ◽  
Input State ◽  
Compound State ◽  
Output System ◽  
Joint Probability Distributions ◽  
Final System ◽  
Mutual Entropy

It has been shown that joint probability distributions of quantum systems generally do not exist, and the key to solving this concern is the compound state invented by Ohya. The Ohya compound state constructed by the Schatten decomposition (i.e., one-dimensional orthogonal projection) of the input state shows the correlation between the states of the input and output systems. In 1983, Ohya formulated the quantum mutual entropy by applying this compound state. Since this mutual entropy satisfies the fundamental inequality, one may say that it represents the amount of information correctly transmitted from the input system through the channel to the output system, and it may play an important role in discussing the efficiency of information transfer in quantum systems. Since the Ohya compound state is separable state, it is important that we must look more carefully into the entangled compound state. This paper is intended as an investigation of the construction of the entangled compound state, and the hybrid entangled compound state is introduced. The purpose of this paper is to consider the validity of the compound states constructing the quantum mutual entropy type complexity. It seems reasonable to suppose that the quantum mutual entropy type complexity defined by using the entangled compound state is not useful to discuss the efficiency of information transmission from the initial system to the final system.

A Note on Entropies for Compound Systems

2015 ◽  
Vol 22 (02) ◽  
pp. 1550010 ◽  
Author(s):  
Noboru Watanabe
Keyword(s):  
Communication Channel ◽  
Quantum Communication ◽  
Input State ◽  
Von Neumann ◽  
Quantum Relative Entropy ◽  
Compound State ◽  
Output System ◽  
The Mean ◽  
Mutual Entropy ◽  
Product Compound

In quantum compound systems, joint (or compound) states usually do not exist [26]. The so-called Ohya compound state was defined by using the von Neumann–Schatten decomposition [23] of an input state and a quantum communication channel. Quantum mutual entropy [10] was introduced by using quantum relative entropy [24] between the Ohya compound state and the trivial (product) compound state on the compound (input and output) system. One of the remarkable results related to state entanglement is the Jamiolkowski isomorphism [5]. In this paper, we use the Jamiolkowski isomorphism for the construction of Ohya compound state and we discuss the existence of a completely positive map between compound entangled states and the Ohya compound states. The efficiency of information transmission is investigated by using the mean entropy and the mean mutual entropy [12, 6] of a connected channel.

scholarly journals A Consistent Track-to-Track Fusion Method Based on Copula Theory

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
Kelin Lu ◽  
K. C. Chang ◽  
Rui Zhou
Keyword(s):  
Probability Distributions ◽  
A Priori ◽  
Joint Probability ◽  
Network Connectivity ◽  
Consistent Estimate ◽  
Fusion Algorithm ◽  
Copula Theory ◽  
Wide Range ◽  
Primary Advantage ◽  
Joint Probability Distributions

This paper addresses the problem of distributed fusion when the conditional independence assumptions on sensor measurements or local estimates are not met. A new data fusion algorithm called Copula fusion is presented. The proposed method is grounded on Copula statistical modeling and Bayesian analysis. The primary advantage of the Copula-based methodology is that it could reveal the unknown correlation that allows one to build joint probability distributions with potentially arbitrary underlying marginals and a desired intermodal dependence. The proposed fusion algorithm requires no a priori knowledge of communications patterns or network connectivity. The simulation results show that the Copula fusion brings a consistent estimate for a wide range of process noises.

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