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

Journal of Physics A Mathematical and Theoretical

Entanglement of three-qubit spin states moving in the gravitational field of a massive body

Fatemeh Ahmadi, Mohammad Mehrafarin

Published Nov 19, 2012• 9 citations
Publisher

Abstract

We study the spin entanglement of a tripartite system consisting of spin- particles in the GHZ and W spin states with and without momentum correlations moving in the gravitational field of a massive body. Considering circular motions of the system around the body, we use spin fidelity as a measure of the change in spin entanglement due to orbiting and describe its behavior as a function of the orbiting velocity and path radius. We find that in the GHZ state momentum correlation always elevates spin entanglement, whereas in the W state it can yield degradation depending on the orbiting velocity. Furthermore, there is a unique circular orbit that leaves the spin entanglement unchanged for both spin states irrespective of the momentum state and orbiting velocity.

DOI
10.1088/1751-8113/45/48/485302

Related papers

Spin entanglement of two spin-\frac{1}{2} particles in a classical gravitational field

B Nasr Esfahani

The effect of a classical gravitational field on the spin entanglement of a system of two spin- particles moving in the curved spacetime is discussed. The system is described by a two-particle Gaussian wave packet represented in the momentum space and both the acceleration of the system and the curvature of the spacetime produce a Wigner rotation acting on the wave packet as it moves along a path in the curved spacetime. By calculating the reduced density operator at a final point, we focus on the spin entanglement of the system. In a spherically symmetric and static gravitational field, for example a charged black hole, there can be particular paths on which the Wigner rotation is trivial and so the initial reduced density matrix remains intact. This causes the spin entanglement to be invariant during the motion. The spin entanglement descends to zero by increasing the angular velocity of the mean centroid of the system as well as increasing the proper time during which the centroid moves on its circular path around the center.

arXiv:1010.5107•Journal of Physics A Mathematical and Theoretical•Oct 22, 2010•11 citations

Spin-induced non-geodesic motion, gyroscopic precession, Wigner rotation and EPR correlations of massive spin 1/2 particles in a gravitational field

Paul M. Alsing, G. J. Stephenson, Patrick Kilian

We investigate in a covariant manner the spin-induced non-geodesic motion of massive spin 1/2 particles in an arbitrary gravitational field for trajectories that are initially geodesic when spin is ignored. Using the WKB approximation for the wave function in curved spacetime, we compute the O(hbar) correction to the Wigner rotation of the spin 1/2 particle, whose O(1) contribution is zero on timelike geodesics. We develop conditions for the motion of observers in which the Wigner rotation is null. For the spherically symmetric Schwarzschild metric, we consider specific examples of particle motion in the equatorial plane for (i) circular orbits and (ii) radially infalling trajectories. For the former case we consider the entanglement for a perfectly anti-correlated EPR entangled pair of spins as the separate qubits traverse the circular orbit in same direction.

arXiv:0902.1396•Feb 9, 2009•18 citations

The cosmological constant effect on the quantum entanglement

A. Mohadi, N. Mebarki, M. Boussahel

In Schwarzschild-de Sitter space-time, the effect of a gravitational field near a massive body black hole on the spin entanglement has been studied for two-qubits in the case of triplet and singlet states of a two particles system in a circular geodesic motion. It is found that the effect of the cosmological constant on the robustness of the Wooters concurrence is more important in the triplet state than in the singlet one even in the extended region around the black hole

Journal of Physics Conference Series•Jul 1, 2019•2 citations

Spin Fidelity for Three-qubit Greenberger-Horne-Zeilinger and W States Under Lorentz Transformations

Bahram Nasr Esfahani, Mohsen Aghaee

Constructing the reduced density matrix for a system of three massive spin- $\frac{1}{2}$ particles described by a wave packet with Gaussian momentum distribution and a spin part in the form of GHZ or W state, the fidelity for the spin part of the system is investigated from the viewpoint of moving observers in the jargon of special relativity. Using a numerical approach, it turns out that by increasing the boost speed, the spin fidelity decreases and reaches to a non-zero asymptotic value that depends on the momentum distribution and the amount of momentum entanglement.

•Jan 1, 2010•4 citations

Relativistic entanglement of two massive particles

Nicolai Friis, Reinhold A. Bertlmann, Marcus Huber +1 more

We describe the spin and momentum degrees of freedom of a system of two massive spin-$\frac{1}{2}$ particles as a four-qubit system. Then we explicitly show how the entanglement changes between different partitions of the qubits, when considered by different inertial observers. Although the two particle entanglement corresponding to a partition into Alice's and Bob's subsystems is, as often stated in the literature, invariant under Lorentz boosts, the entanglement with respect to other partitions of the Hilbert space on the other hand, is not. It certainly does depend on the chosen inertial frame and on the initial state considered. The change of entanglement arises, because a Lorentz boost on the momenta of the particles causes a Wigner rotation of the spin, which in certain cases entangles the spin with the momentum states. We systematically investigate the situation for different classes of initial spin states and different partitions of the four-qubit space. Furthermore, we study the behavior of Bell inequalities for different observers and demonstrate how the maximally possible degree of violation, using the Pauli-Lubanski spin observable, can be recovered by any inertial observer.

arXiv:0912.4863•Physical Review A•Apr 30, 2010•113 citations

RELATIVISTIC ENTANGLEMENT FOR SPINS AND MOMENTA OF A MASSIVE THREE-PARTICLE SYSTEM

BAHRAM NASR ESFAHANI, Mohsen Aghaee

Lorentz transformation of the spin density matrix as well as the momentum density matrix for a quantum system of three massive spin-1/2 particles that have an appropriate discrete momentum distribution is investigated. In a rest frame, both the spin and the momentum parts are supposed to be maximally entangled as the Greenberger–Horne–Zeilinger state. Provided the particles move with sufficiently high speeds, we can find boosts that completely remove both the spin and momentum entanglements. We can even find boosts that completely preserve both entanglements. For the considered boosts, there is no mixing between the spin and the momentum parts.

International Journal of Quantum Information•May 25, 2011•3 citations
We study the spin entanglement of a tripartite system consisting of spin- particles in the GHZ and W spin states with and without momentum correlations moving in the gravitational field of a massive body. Considering circular motions of the system around the body, we use spin fidelity as a measure of the change in spin entanglement due to orbiting and describe its behavior as a function of the orbiting velocity and path radius. We find that in the GHZ state momentum correlation always elevates spin entanglement, whereas in the W state it can yield degradation depending on the orbiting velocity. Furthermore, there is a unique circular orbit that leaves the spin entanglement unchanged for both spin states irrespective of the momentum state and orbiting velocity.
The effect of a classical gravitational field on the spin entanglement of a system of two spin- particles moving in the curved spacetime is discussed. The system is described by a two-particle Gaussian wave packet represented in the momentum space and both the acceleration of the system and the curvature of the spacetime produce a Wigner rotation acting on the wave packet as it moves along a path in the curved spacetime. By calculating the reduced density operator at a final point, we focus on the spin entanglement of the system. In a spherically symmetric and static gravitational field, for example a charged black hole, there can be particular paths on which the Wigner rotation is trivial and so the initial reduced density matrix remains intact. This causes the spin entanglement to be invariant during the motion. The spin entanglement descends to zero by increasing the angular velocity of the mean centroid of the system as well as increasing the proper time during which the centroid moves on its circular path around the center.
We investigate in a covariant manner the spin-induced non-geodesic motion of massive spin 1/2 particles in an arbitrary gravitational field for trajectories that are initially geodesic when spin is ignored. Using the WKB approximation for the wave function in curved spacetime, we compute the O(hbar) correction to the Wigner rotation of the spin 1/2 particle, whose O(1) contribution is zero on timelike geodesics. We develop conditions for the motion of observers in which the Wigner rotation is null. For the spherically symmetric Schwarzschild metric, we consider specific examples of particle motion in the equatorial plane for (i) circular orbits and (ii) radially infalling trajectories. For the former case we consider the entanglement for a perfectly anti-correlated EPR entangled pair of spins as the separate qubits traverse the circular orbit in same direction.
Constructing the reduced density matrix for a system of three massive spin- 12\frac{1}{2}21​ particles described by a wave packet with Gaussian momentum distribution and a spin part in the form of GHZ or W state, the fidelity for the spin part of the system is investigated from the viewpoint of moving observers in the jargon of special relativity. Using a numerical approach, it turns out that by increasing the boost speed, the spin fidelity decreases and reaches to a non-zero asymptotic value that depends on the momentum distribution and the amount of momentum entanglement.
We describe the spin and momentum degrees of freedom of a system of two massive spin-12\frac{1}{2}21​ particles as a four-qubit system. Then we explicitly show how the entanglement changes between different partitions of the qubits, when considered by different inertial observers. Although the two particle entanglement corresponding to a partition into Alice's and Bob's subsystems is, as often stated in the literature, invariant under Lorentz boosts, the entanglement with respect to other partitions of the Hilbert space on the other hand, is not. It certainly does depend on the chosen inertial frame and on the initial state considered. The change of entanglement arises, because a Lorentz boost on the momenta of the particles causes a Wigner rotation of the spin, which in certain cases entangles the spin with the momentum states. We systematically investigate the situation for different classes of initial spin states and different partitions of the four-qubit space. Furthermore, we study the behavior of Bell inequalities for different observers and demonstrate how the maximally possible degree of violation, using the Pauli-Lubanski spin observable, can be recovered by any inertial observer.
Lorentz transformation of the spin density matrix as well as the momentum density matrix for a quantum system of three massive spin-1/2 particles that have an appropriate discrete momentum distribution is investigated. In a rest frame, both the spin and the momentum parts are supposed to be maximally entangled as the Greenberger–Horne–Zeilinger state. Provided the particles move with sufficiently high speeds, we can find boosts that completely remove both the spin and momentum entanglements. We can even find boosts that completely preserve both entanglements. For the considered boosts, there is no mixing between the spin and the momentum parts.