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Journal of Physics G Nuclear and Particle Physics

Entanglement of 1s0d-shell nucleon pairs

EDWARD KWAŚNIEWICZ

Published Dec 3, 2013• 9 citations
Publisher

Abstract

The entanglement of pure states of 1s0d-shell nucleon pairs has been studied. The Slater decomposition theorem has been used to verify if any pure state of a nucleon pair is an entangled state. The von Neumann entropy of the partial density matrix has been employed to quantify the entanglement of the 1s0d-shell nucleon pairs. Results of calculations have evidenced that the isospin T = 1 states of the 1s0d-shell nucleon pairs are strongly entangled.

DOI
10.1088/0954-3899/41/1/015107

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•Jan 1, 2021•21 citations
The entanglement of pure states of 1s0d-shell nucleon pairs has been studied. The Slater decomposition theorem has been used to verify if any pure state of a nucleon pair is an entangled state. The von Neumann entropy of the partial density matrix has been employed to quantify the entanglement of the 1s0d-shell nucleon pairs. Results of calculations have evidenced that the isospin T = 1 states of the 1s0d-shell nucleon pairs are strongly entangled.
Entanglement of 1p0f1p0f1p0f-shell Nucleon Pairs
The entanglement of pure states of the [Formula: see text]-, [Formula: see text]- and [Formula: see text]-shell nucleon pairs has been studied. The von Neumann entropy of the partial density matrix has been employed to quantify the entanglement of the [Formula: see text]-, [Formula: see text]- and [Formula: see text]-shell nucleon pairs. The Slater decomposition theorem has been used to verify if any pure state of a nucleon pair is an entangled state. Results of calculations have evidenced that a dominant part of the isospin [Formula: see text] proton–neutron states of the [Formula: see text]-, [Formula: see text]- and [Formula: see text]-shell nucleon pairs, respectively, are strongly entangled. It is shown that the calculated data are a source of valuable information on the spin quantum numbers of the entangled protons from two-proton decay.
Abstract In this study, we explore the entanglement and correlation in two-nucleon systems using isospin formalism. With the help of Slater decomposition, we derive analytical expressions for various entanglement measures. Specifically, we analyse the one- and two-mode entropies, mutual informations, and a basis-independent characteristic known as the one-body entanglement entropy. To understand the impact of pairing, we consider interactions involving isovector and isoscalar L = 0 pairing terms. Our findings show that certain pairing interactions can maximize one-body entanglement entropy of ground states when both total angular momentum and total isospin have zero projections. We provide numerical examples for the sd shell and explore the mutual informations in LS coupled and jj coupled single-particle bases. We find that the shell structure and angular momentum coupling significantly impact the measures of entanglement. We outline the implications of conserving angular momentum and isospin on one-mode entropies, irrespective of particle number.
Abstract We examine mode entanglement and correlation of two fermionic particles analytically and numerically. We study the one- and two-mode entropies and a global characteristic, the one-body entanglement entropy considering angular momentum coupled state with a single configuration. We show that with rearrangement of the single-particle orbitals the Slater decomposition can be obtained which can also be applied for configuration mixing subject to special restriction. With the help of the Slater decomposition, we derive analytical expressions for the entanglement measures, which becomes very simple for zero total angular momentum. The Slater decomposition allows us to define associated modes, and it turns out that they have identical one- and two-mode entropies. Furthermore, we show that specific single configurations describe maximally entangled states when the total angular momentum is zero. The numerical shell model study of two valence neutrons in the sd shell is revealed that the one-body entanglement entropy of the ground state is close to the maximal value, and the associated modes have the largest mutual information.
Abstract Quantum entanglement offers a unique perspective into the underlying structure of strongly-correlated systems such as atomic nuclei. In this paper, we use quantum information tools to analyze the structure of light and medium-mass berillyum, oxygen, neon and calcium isotopes within the nuclear shell model. We use different entanglement metrics, including single-orbital entanglement, mutual information, and von Neumann entropies for different equipartitions of the shell-model valence space and identify mode-entanglement patterns related to the energy, angular momentum and isospin of the nuclear single-particle orbitals. We observe that the single-orbital entanglement is directly related to the number of valence nucleons and the energy structure of the shell, while the mutual information highlights signatures of proton–proton and neutron–neutron pairing, as well as nuclear deformation. Proton and neutron orbitals are weakly entangled by all measures, and in fact have the lowest von Neumann entropies among all possible equipartitions of the valence space. In contrast, orbitals with opposite angular momentum projection have relatively large entropies, especially in spherical nuclei. This analysis provides a guide for designing more efficient quantum algorithms for the noisy intermediate-scale quantum era.
We examine the mode entanglement and correlation of two fermionic particles. We study the one- and two-mode entropy and a global characteristic, the one-body entanglement entropy. We consider not only angular momentum coupled states with single configuration but use the configuration interaction method. With the help of the Slater decomposition, we derive analytical expressions for the entanglement measures. We show that when the total angular momentum is zero specific single configurations describe maximally entangled states. It turns out that for a finite number of associated modes the one- and two-mode entropies have identical values. In the shell model framework, we numerically study two valence neutrons in the sdsdsd shell. The one-body entanglement entropy of the ground state is close to the maximal value and the associated modes have the largest mutual information.