Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2006.07448 · Journal of Physics G Nuclear and Particle Physics

Entanglement and correlation in two-nucleon systems

A T Kruppa, J Kovács, P Salamon, Ö Legeza

Published Oct 20, 2020• 32 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1088/1361-6471/abc2dd

Related papers

Entanglement and correlation in two-nucleon systems

Kruppa, András Tibor, Kovács, József, Salamon, Péter +1 more

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 $sd$ 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.

•Jan 1, 2021•21 citations

Mode entanglement and isospin pairing in two-nucleon systems

J. Kovács, András T. Kruppa, Örs Legeza +1 more

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.

arXiv:2409.12583•Journal of Physics G Nuclear and Particle Physics•Nov 15, 2024•4 citations

Entanglement in fermion systems

N. Gigena, R. Rossignoli

We analyze the problem of quantifying entanglement in pure and mixed states of fermionic systems with a fixed number parity yet not necessarily a fixed particle number. The mode entanglement between one single-particle level and its orthogonal complement is first considered, and an entanglement entropy for such a partition of a particular basis of the single-particle Hilbert space $\mathcal{H}$ is defined. The sum over all single-particle modes of this entropy is introduced as a measure of the total entanglement of the system with respect to the chosen basis and it is shown that its minimum over all bases of $\mathcal{H}$ is a function of the one-body density matrix. Furthermore, we show that if minimization is extended to all bases related through a Bogoliubov transformation, then the entanglement entropy is a function of the generalized one-body density matrix. These results are then used to quantify entanglement in fermion systems with four single-particle levels. For general pure states of such a system a closed expression for the fermionic concurrence is derived, which generalizes the Slater correlation measure defined by J. Schliemann et al. [Phys. Rev. A 64, 022303 (2001)], implying that particle entanglement may be seen as minimum mode entanglement. It is also shown that the entanglement entropy defined before is related to this concurrence by an expression analogous to that in the two-qubit case. For mixed states of this system the convex roof extension of the previous concurrence and entanglement entropy is evaluated analytically, extending the results in previous reference to general states.

arXiv:1509.05970•Physical Review A•Oct 23, 2015•65 citations

Fermionic entanglement and quantum correlation measures in molecules

J. Garcia, J. A. Cianciulli, R. Rossignoli

We analyze fermionic entanglement and correlation measures in the ground and the low temperature thermal state of the water molecule as a function of the internuclear distance in the context of the full configuration interaction approach. The aim is to obtain a general entanglement based characterization of the electronic eigenstates. We consider first the spin-up - spin-down partition and the associated Schmidt decomposition, examining the total up-down entanglement of the electronic wave function. We then consider the one- and two-body entanglement derived from the one- and two-body reduced density matrices (DMs), which measure both the deviation of the state from a Slater Determinant (SD) as well as the up-down correlation at the two-body level. All blocks of these DMs are examined. We also introduce and analyze new measures like the up-down two-body mutual information and two types of two-body negativities, the latter measuring the "inner" entanglement of the reduced two-body DMs, i.e., their deviation from a convex mixture of SDs. Finally, the dissociation limit is also analyzed, considering both the exact ground state (GS) as well as the thermal state in the zero temperature limit, representing the projector onto the "GS band" of almost degenerate lowest lying eigenstates.

quant-pharXiv:2604.07633•Apr 10, 2026•0 citations

Fermionic entanglement in superconducting systems

Martina Di Tullio, N. Gigena, R. Rossignoli

We examine distinct measures of fermionic entanglement in the exact ground state of a finite superconducting system. It is first shown that global measures such as the one-body entanglement entropy, which represents the minimum relative entropy between the exact ground state and the set of fermionic Gaussian states, exhibit a close correlation with the BCS gap, saturating in the strong superconducting regime. The same behavior is displayed by the bipartite entanglement between the set of all single-particle states $k$ of positive quasimomenta and their time-reversed partners $\overline{k}$. In contrast, the entanglement associated with the reduced density matrix of four single-particle modes $k,\overline{k}, {k}^{\ensuremath{'}},{\overline{k}}^{\ensuremath{'}}$, which can be measured through a properly defined fermionic concurrence, exhibits a different behavior, showing a peak in the vicinity of the superconducting transition for states $k,{k}^{\ensuremath{'}}$ close to the Fermi level and becoming small in the strong coupling regime. In the latter, such reduced state exhibits, instead, a finite mutual information and quantum discord. While the first measures can be correctly estimated with the BCS approximation, the previous four-level concurrence lies strictly beyond the latter, requiring at least a particle-number projected BCS treatment for its description. Formal properties of all previous entanglement measures are as well discussed.

arXiv:1803.08883•Physical Review A•Jun 11, 2018•22 citations

Quantum entanglement patterns in the structure of atomic nuclei within the nuclear shell model

Axel Pérez-Obiol, Sergi Masot-Llima, A. M. Romero +4 more

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.

arXiv:2307.05197•The European Physical Journal A•Oct 25, 2023•36 citations
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.
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.
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 analyze the problem of quantifying entanglement in pure and mixed states of fermionic systems with a fixed number parity yet not necessarily a fixed particle number. The mode entanglement between one single-particle level and its orthogonal complement is first considered, and an entanglement entropy for such a partition of a particular basis of the single-particle Hilbert space H\mathcal{H}H is defined. The sum over all single-particle modes of this entropy is introduced as a measure of the total entanglement of the system with respect to the chosen basis and it is shown that its minimum over all bases of H\mathcal{H}H is a function of the one-body density matrix. Furthermore, we show that if minimization is extended to all bases related through a Bogoliubov transformation, then the entanglement entropy is a function of the generalized one-body density matrix. These results are then used to quantify entanglement in fermion systems with four single-particle levels. For general pure states of such a system a closed expression for the fermionic concurrence is derived, which generalizes the Slater correlation measure defined by J. Schliemann et al. [Phys. Rev. A 64, 022303 (2001)], implying that particle entanglement may be seen as minimum mode entanglement. It is also shown that the entanglement entropy defined before is related to this concurrence by an expression analogous to that in the two-qubit case. For mixed states of this system the convex roof extension of the previous concurrence and entanglement entropy is evaluated analytically, extending the results in previous reference to general states.
We analyze fermionic entanglement and correlation measures in the ground and the low temperature thermal state of the water molecule as a function of the internuclear distance in the context of the full configuration interaction approach. The aim is to obtain a general entanglement based characterization of the electronic eigenstates. We consider first the spin-up - spin-down partition and the associated Schmidt decomposition, examining the total up-down entanglement of the electronic wave function. We then consider the one- and two-body entanglement derived from the one- and two-body reduced density matrices (DMs), which measure both the deviation of the state from a Slater Determinant (SD) as well as the up-down correlation at the two-body level. All blocks of these DMs are examined. We also introduce and analyze new measures like the up-down two-body mutual information and two types of two-body negativities, the latter measuring the "inner" entanglement of the reduced two-body DMs, i.e., their deviation from a convex mixture of SDs. Finally, the dissociation limit is also analyzed, considering both the exact ground state (GS) as well as the thermal state in the zero temperature limit, representing the projector onto the "GS band" of almost degenerate lowest lying eigenstates.
We examine distinct measures of fermionic entanglement in the exact ground state of a finite superconducting system. It is first shown that global measures such as the one-body entanglement entropy, which represents the minimum relative entropy between the exact ground state and the set of fermionic Gaussian states, exhibit a close correlation with the BCS gap, saturating in the strong superconducting regime. The same behavior is displayed by the bipartite entanglement between the set of all single-particle states kkk of positive quasimomenta and their time-reversed partners k‾\overline{k}k. In contrast, the entanglement associated with the reduced density matrix of four single-particle modes $k,\overline{k}, {k}^{\ensuremath{'}},{\overline{k}}^{\ensuremath{'}}$, which can be measured through a properly defined fermionic concurrence, exhibits a different behavior, showing a peak in the vicinity of the superconducting transition for states $k,{k}^{\ensuremath{'}}$ close to the Fermi level and becoming small in the strong coupling regime. In the latter, such reduced state exhibits, instead, a finite mutual information and quantum discord. While the first measures can be correctly estimated with the BCS approximation, the previous four-level concurrence lies strictly beyond the latter, requiring at least a particle-number projected BCS treatment for its description. Formal properties of all previous entanglement measures are as well discussed.
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.