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

Physica Scripta

Nuclear quadrupole resonance of spin 3/2 and entangled two-qubit states

G. B. Furman, S. D. Goren, V. Meerovich, Vladimir Sokolovsky

Published Sep 15, 2015• 8 citations
Publisher

Abstract

A single spin- possessing a quadrupole moment and placed in a non-uniform electric field, is isomorphic to a system of two spins of which can be represented as two qubits. To create these qubits, the degeneracy of the energy levels is removed by applying two radio-frequency fields with different phases and directions. The properties of entanglement between two qubits are studied. We analyze the concurrence, the entropy of entanglement, and fluctuations of the entropy in the pure and mixed states. Concurrence and entropy of entanglement in a mixed state increase with decreasing temperature and approach to their values in a pure state. For a nucleus Cu in high temperature superconductor the estimation of the temperature, at which entanglement appears, gives 0.8 μ K.

DOI
10.1088/0031-8949/90/10/105301

Related papers

Entanglement between states of single quadrupole nuclear spin

G. B. Furman, V. Meerovich, Vladimir Sokolovsky

We study entanglement between quantum states of multi level spin system of a single particle considering a nucleus with spin 3/2 in both the internal electric field gradient and the external magnetic field. It was shown that entanglement is achieved by applying a magnetic field to a single particle at low temperature (~ 5 mK). In this temperature range, the numerical calculation revealed the coincidence between magnetization and concurrence. As a result, the magnetization can be used as an entanglement witness for such systems.

arXiv:1005.2886•May 17, 2010•0 citations

Two qubits in pure nuclear quadrupole resonance

G. B. Furman, S. D. Goren, V. Meerovich +1 more

It is shown theoretically that by the use of two radio-frequency fields of the same resonance frequency but with the different phases and directions the degeneracy of the energy spectrum of a spin system with I = 3/2 is removed. This leads to four non-degenerate spin states which can be used as a platform for quantum computing. The feasibility of quantum computing based on a pure (without DC magnetic fields) nuclear quadrupole resonance technique is investigated in detail. Various quantum logic gates can be constructed by using different excitation techniques allowing different manipulations with the spin system states. Three realizations of quantum logic gates are considered: the application of an additional magnetic field with the resonance frequency, the amplitude modulation of one of the applied RF fields by the resonance frequency field, and the level-crossing method. It is shown that the probabilities of the resonance transitions depend on the method of excitation and on the direction of the excitation field. Feasibility of quantum computing is demonstrated with the examples of constructing a controlled-NOT logic gate using the resonance excitation technique and SWAP and NOT2 logic gates using the level-crossing method.

Journal of Physics Condensed Matter•Sep 5, 2002•13 citations

Fictitious spin-12 operators and correlations in quadrupole nuclear spin system

G. B. Furman, S. D. Goren, V. Meerovich +1 more

The Hamiltonian and the spin operators for a spin 3/2 are represented in the basis formed by the Kronecker productions of the [Formula: see text] Pauli matrices. This reformulation allows us to represent a spin 3/2 as a system of two coupled fictitious spins 1/2. Correlations between these fictitious spins are studied using well-developed methods. We investigate the temperature and field dependences of correlations, such as mutual information, classical correlations, entanglement, and geometric and quantum discords in the fictitious spin-1/2 system describing a nuclear spin 3/2 which is placed in magnetic and inhomogeneous electric fields. It is shown that the correlations between the fictitious spins demonstrate properties which differ from those of real two-spin systems. In contrast to real systems all the correlations between the fictitious spins do not vanish with increasing external magnetic field; at a high magnetic field the correlations tend to their limiting values. Classical correlations, quantum and geometric discords reveal a pronounced asymmetry relative to the measurements on subsystems (fictitious spins) even in a uniform magnetic field and at symmetrical EFG, [Formula: see text]. The correlations depend also on the distribution of external charges, on the parameter of symmetry [Formula: see text]. At [Formula: see text] quantum and geometric discords have finite values in a zero magnetic field. The proposed approach may be useful in analysis of properties of particles with larger angular momentum, can provide the way to discover new physical phenomenon of quantum correlations, and can be a useful tool for similar definitions of other physical quantities of complex systems.

International Journal of Quantum Information•Jan 9, 2018•5 citations

Entanglement of bipartite partly non-orthogonal 1 2 -spin coherent states

Mostafa Mansour, Zakaria Dahbi

Abstract We investigate the entanglement of a bipartite partly non-orthogonal state of the form | ϕ ⟩ = u | ξ ⟩ 1 ⊗ | 1 ⟩ 2 + v | ξ ⟩ 1 ⊗ | 0 ⟩ 2 + w | ξ ′ ⟩ 1 ⊗ | 1 ⟩ 2 + z | ξ ′ ⟩ 1 ⊗ | 0 ⟩ 2 through 1 2 -spin coherent states by adopting the concurrence as a measure to quantify the degree of entanglement of the two-qubit system. After, we study the amount of entanglement of mixed states represented by a statistical mixture of partly non-orthogonal bipartite pure states. We also express the lower and upper bounds of the squared concurrence of mixed states in terms of the amplitudes of spin coherent states.

Laser Physics•Jun 29, 2020•21 citations

Two-qubit-entanglement in matter created by entangled-photon pairs: A perturbative analysis

Upendra Harbola, Luca Candelori, John R. Klein +2 more

We study entanglement created between two isolated qubits by interaction with entangled-photon pairs obtained by parametric down-conversion of a laser pump field. The induced entanglement is quantified using the mixed state Concurrence proposed by Wootters et al. [Phys. Rev. Lett. 78, 5022 (1997)]. A universal value of qubit-entanglement, which is independent on the photon-pair wavefunction is identified to leading order in the qubit–field interaction and the pump field amplitude. The qubit entanglement decreases at higher laser pump intensities due to interference between the entangled photon pairs, which creates excitations in the qubit system. Maximal Concurrence is produced by only generating coherences between the ground and the highest excited qubit states.

AVS Quantum Science•Sep 1, 2024•2 citations

Pure NQR Quantum Computing

G. B. Furman, S. D. Goren

It is shown that pure NQR can be utilized as a platform for quantum computing without applying a high external magnetic field. By exciting each resonance transition between quadrupole energy levels with two radio-frequency fields differing in phase and direction, the double degeneracy of the spin energy spectrum in an electric field gradient is removed. As an example, in the case of I = 7/2 (nuclei 133Cs or 123Sb) the energy spectrum has eight levels which can be used as three qubits.

Zeitschrift für Naturforschung A•Jul 1, 2002•19 citations
A single spin- possessing a quadrupole moment and placed in a non-uniform electric field, is isomorphic to a system of two spins of which can be represented as two qubits. To create these qubits, the degeneracy of the energy levels is removed by applying two radio-frequency fields with different phases and directions. The properties of entanglement between two qubits are studied. We analyze the concurrence, the entropy of entanglement, and fluctuations of the entropy in the pure and mixed states. Concurrence and entropy of entanglement in a mixed state increase with decreasing temperature and approach to their values in a pure state. For a nucleus Cu in high temperature superconductor the estimation of the temperature, at which entanglement appears, gives 0.8 μ K.
We study entanglement between quantum states of multi level spin system of a single particle considering a nucleus with spin 3/2 in both the internal electric field gradient and the external magnetic field. It was shown that entanglement is achieved by applying a magnetic field to a single particle at low temperature (~ 5 mK). In this temperature range, the numerical calculation revealed the coincidence between magnetization and concurrence. As a result, the magnetization can be used as an entanglement witness for such systems.
It is shown theoretically that by the use of two radio-frequency fields of the same resonance frequency but with the different phases and directions the degeneracy of the energy spectrum of a spin system with I = 3/2 is removed. This leads to four non-degenerate spin states which can be used as a platform for quantum computing. The feasibility of quantum computing based on a pure (without DC magnetic fields) nuclear quadrupole resonance technique is investigated in detail. Various quantum logic gates can be constructed by using different excitation techniques allowing different manipulations with the spin system states. Three realizations of quantum logic gates are considered: the application of an additional magnetic field with the resonance frequency, the amplitude modulation of one of the applied RF fields by the resonance frequency field, and the level-crossing method. It is shown that the probabilities of the resonance transitions depend on the method of excitation and on the direction of the excitation field. Feasibility of quantum computing is demonstrated with the examples of constructing a controlled-NOT logic gate using the resonance excitation technique and SWAP and NOT2 logic gates using the level-crossing method.
The Hamiltonian and the spin operators for a spin 3/2 are represented in the basis formed by the Kronecker productions of the [Formula: see text] Pauli matrices. This reformulation allows us to represent a spin 3/2 as a system of two coupled fictitious spins 1/2. Correlations between these fictitious spins are studied using well-developed methods. We investigate the temperature and field dependences of correlations, such as mutual information, classical correlations, entanglement, and geometric and quantum discords in the fictitious spin-1/2 system describing a nuclear spin 3/2 which is placed in magnetic and inhomogeneous electric fields. It is shown that the correlations between the fictitious spins demonstrate properties which differ from those of real two-spin systems. In contrast to real systems all the correlations between the fictitious spins do not vanish with increasing external magnetic field; at a high magnetic field the correlations tend to their limiting values. Classical correlations, quantum and geometric discords reveal a pronounced asymmetry relative to the measurements on subsystems (fictitious spins) even in a uniform magnetic field and at symmetrical EFG, [Formula: see text]. The correlations depend also on the distribution of external charges, on the parameter of symmetry [Formula: see text]. At [Formula: see text] quantum and geometric discords have finite values in a zero magnetic field. The proposed approach may be useful in analysis of properties of particles with larger angular momentum, can provide the way to discover new physical phenomenon of quantum correlations, and can be a useful tool for similar definitions of other physical quantities of complex systems.
Abstract We investigate the entanglement of a bipartite partly non-orthogonal state of the form | ϕ ⟩ = u | ξ ⟩ 1 ⊗ | 1 ⟩ 2 + v | ξ ⟩ 1 ⊗ | 0 ⟩ 2 + w | ξ ′ ⟩ 1 ⊗ | 1 ⟩ 2 + z | ξ ′ ⟩ 1 ⊗ | 0 ⟩ 2 through 1 2 -spin coherent states by adopting the concurrence as a measure to quantify the degree of entanglement of the two-qubit system. After, we study the amount of entanglement of mixed states represented by a statistical mixture of partly non-orthogonal bipartite pure states. We also express the lower and upper bounds of the squared concurrence of mixed states in terms of the amplitudes of spin coherent states.
We study entanglement created between two isolated qubits by interaction with entangled-photon pairs obtained by parametric down-conversion of a laser pump field. The induced entanglement is quantified using the mixed state Concurrence proposed by Wootters et al. [Phys. Rev. Lett. 78, 5022 (1997)]. A universal value of qubit-entanglement, which is independent on the photon-pair wavefunction is identified to leading order in the qubit–field interaction and the pump field amplitude. The qubit entanglement decreases at higher laser pump intensities due to interference between the entangled photon pairs, which creates excitations in the qubit system. Maximal Concurrence is produced by only generating coherences between the ground and the highest excited qubit states.