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International Journal of Modern Physics E

Entanglement of 0p-, 1s0d- and 1p0f-shell nucleon pairs

EDWARD KWAŚNIEWICZ, Dariusz Kurzyk

Published Apr 16, 2017• 8 citations
Publisher

Abstract

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.

DOI
10.1142/s0218301317500239

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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.
Entanglement of 1p0f1p0f1p0f-shell Nucleon Pairs
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.
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.
We investigate polarization states of the outgoing neutron-proton (npnpnp) pair in elastic polarized neutron and proton scattering, aiming to find unambiguous evidence for entanglement of their spin states. To obtain complete information about these states, we calculate, using the high precision nucleon-nucleon potential AV18, the final polarizations of the neutron and proton as well as their spin correlation coefficients, which unequivocally define the corresponding spin density matrix. We compute all terms contributing to polarizations and spin correlations, e.g. not only induced polarizations and correlations resulting from unpolarized npnpnp scattering, but also contributions from single polarization and correlation transfers from individual polarized incoming nucleons, and, for the first time, allotment to both quantities stemming from a doubly spin polarized initial state. We find that for the most part the final spin states are statistical mixture of states.The only pure states occur for highly polarized incoming neutrons and protons with maximal polarizations. By quantifying the degree of entanglement through entanglement power and concurrence, we observed that the entanglement of impure final states increases with energy. Among the pure spin states resulting from incoming states with maximal neutron and proton polarizations, we found, at Elab=100E_{lab}=100Elab​=100~MeV, cases of strongly entangled Bell-type states with only a small admixture of entanglement-spoiling contributions.
We investigate polarization states of the outgoing neutron-proton (npnpnp) pair in elastic polarized neutron and proton scattering, aiming to find unambiguous evidence for entanglement of their spin states. To obtain complete information about these states, we calculate, using the high-precision nucleon-nucleon potential AV18, the final polarizations of the neutron and proton as well as their spin correlation coefficients, which unequivocally define the corresponding spin density matrix. We compute all terms contributing to polarizations and spin correlations, e.g., not only induced polarizations and correlations resulting from unpolarized npnpnp scattering but also contributions from single polarization and correlation transfers from individual polarized incoming nucleons and, for the first time, allotment to both quantities stemming from a doubly spin polarized initial state. We find that for the most part the final spin states are statistical mixture of states. The only pure states occur for highly polarized incoming neutrons and protons with maximal polarizations. By quantifying the degree of entanglement through entanglement power and concurrence, we observed that the entanglement of impure final states increases with energy. Among the pure spin states resulting from incoming states with maximal neutron and proton polarizations, we found, at Elab=100{E}_{\mathrm{lab}}=100Elab​=100 MeV, cases of strongly entangled Bell-type states with only a small admixture of entanglement-spoiling contributions.