Abstract
We study the correlation of the ground state of an N-particle Moshinsky model by computing the Shannon entropy in both position and momentum spaces. We have derived the Shannon entropy and mutual information with analytical forms of such an N-particle Moshinsky model, and this helps us test the entropic uncertainty principle. The Shannon entropy in position space decreases as interaction strength increases. However, Shannon entropy in momentum space has the opposite trend. Shannon entropy of the whole system satisfies the equality of entropic uncertainty principle. Our results also indicate that, independent of the sizes of the two subsystems, the mutual information increases monotonically as the interaction strength increases.
Highlights
Since understanding the correlation of quantum many body problems is crucial to quantum information processes, and quantum systems described as harmonically confined systems with tunable interaction parameters are promising for development in quantum information processes, such quantum systems provide us a motivation to study correlation in a solvable many body system—anN-particle Moshinsky model.In the Moshinsky model [1], the system is confined in harmonic traps and inter-particle interaction takes a harmonic form
We focus on three topics: understanding statistical correlations, testing the entropic uncertainty principle, and comparing the statistical correlation to the quantum correlation of an N-particle Moshinsky model
In [2], the definition of Shannon entropy, one-particle Shannon entropy and mutual information in position space is given, and we extend the definition to a system with N particles as follows: Spos = − dx1...dxN Γ( x1,..., xN ) ln Γ( x1,..., xN ), ( p)
Summary
Since understanding the correlation of quantum many body problems is crucial to quantum information processes, and quantum systems described as harmonically confined systems with tunable interaction parameters are promising for development in quantum information processes, such quantum systems provide us a motivation to study correlation in a solvable many body system—an. Smom and S mom are Shannon entropy of the whole system calculated by Λ (q1 ,..., qN ) , the probability density function in momentum space, and the p-particle. The entropic uncertainty principle has been investigated in [20], and entropic uncertainty relations in atomic systems were discussed in some studies [2,21] In this model, by calculating Shannon entropies in position and momentum space, we can test the entropic uncertainty principle [20], as:. For the third topic, comparing to Shannon entropy, von Neumann entropy is a measure of quantum information and is widely used in many atomic systems [22,23,24,25,26,27].
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