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

Entanglement dynamics for two interacting spins

Novaes, M

Published Oct 20, 2005• 15 citations
OpenAlex

Abstract

We study the dynamical generation of entanglement for a very simple system: a pair of interacting spins, s1 and s2, in a constant magnetic field. Two different situations are considered:(a) s1 ->\\infty, s2 = 1/2 and (b) s1 = s2 ->\\infty, corresponding, respectively, to a quantum degree of freedom coupled to a semiclassical one (a qubit in contact with an environment) and a fully semiclassical system, which in this case displays chaotic behavior. Relations between quantum entanglement and classical dynamics are investigated.

Related papers

Lyapunov Generation of Entanglement and the Correspondence Principle

Cyril Petitjean, Philippe Jacquod

We show how a classically vanishing interaction generates entanglement between two initially nonentangled particles, without affecting their classical dynamics. For chaotic dynamics, the rate of entanglement is shown to saturate at the Lyapunov exponent of the classical dynamics as the interaction strength increases. In the saturation regime, the one-particle Wigner function follows classical dynamics better and better as one goes deeper and deeper in the semiclassical limit. This demonstrates that quantum-classical correspondence at the microscopic level does not require coupling to a large number of external degrees of freedom.

arXiv:quant-ph/0510157•Physical Review Letters•Nov 10, 2006•37 citations

Semiclassical Time Evolution of the Reduced Density Matrix and Dynamically Assisted Generation of Entanglement for Bipartite Quantum Systems

Philippe Jacquod

Two particles, initially in a product state, become entangled when they come together and start to interact. Using semiclassical methods, we calculate the time evolution of the corresponding reduced density matrix rho(1), obtained by integrating out the degrees of freedom of one of the particles. We find that entanglement generation sensitively depends (i) on the interaction potential, especially on its strength and range, and (ii) on the nature of the underlying classical dynamics. Under general statistical assumptions, and for short-ranged interaction potentials, we find that P(t) decays exponentially fast in a chaotic environment, whereas it decays only algebraically in a regular system. In the chaotic case, the decay rate is given by the golden rule spreading of one-particle states due to the two-particle coupling, but cannot exceed the system's Lyapunov exponent.

arXiv:quant-ph/0308099•Physical Review Letters•Apr 13, 2004•81 citations

Entanglement dephasing dynamics driven by a bath of spins

Jie Xu, Jun Jing, Ting Yu

We have studied the entanglement dynamics for a two-qubit system coupled to a spin environment of different configurations by a z–x-type interaction. Quantum dynamics of the models considered in this paper is solved analytically. Moreover, we show that simple and concise results may be obtained when certain approximations are properly made. Our purpose is to find out how the entanglement of a central spin system is affected by the pre-designed factors of the system and its environment, such as their initial states and the coupling constants between the system and its environment. Clearly, how the system is coupled to its environment will inevitably change the feature of entanglement evolution of the central spin system. Our major findings include the following: (i) the entanglement of the system of interest is sensitive to the number of spins in the environment, (ii) the initial states of the environment can profoundly affect the dynamics of the entanglement of the central spin system and (iii) the entangled environment can speed up the decay and revival of the entanglement of the central spin system. Our results exhibit some interesting features that have not been found for a bosonic environment.

arXiv:1009.2128•Journal of Physics A Mathematical and Theoretical•Apr 5, 2011•13 citations

Entanglement dynamics via semiclassical propagators in systems of two spins

A. D. Ribeiro, R. M. Angelo

We analyze the dynamical generation of entanglement in systems of two interacting spins initially prepared in a product of spin coherent states. For arbitrary time-independent Hamiltonians, we derive a semiclassical expression for the purity of the reduced density matrix as a function of time. The final formula, subsidiary to the linear entropy, shows that the short-time dynamics of entanglement depends exclusively on the stability of trajectories governed by the underlying classical Hamiltonian. In addition, this semiclassical measure is shown to reproduce the general properties of its quantum counterpart and give the expected result in the large spin limit. The accuracy of the semiclassical formula is further illustrated in a problem of phase exchange for two particles of spin $j$.

arXiv:1202.5144•Physical Review A•May 17, 2012•7 citations

Decoherence of qubits interacting with a nonlinear dissipative classical or quantum system

Nikola Burić

Quantum trajectories given by the quantum state diffusion theory are used to study the dynamics of a pair of qubits interacting with the quantized Duffing oscillator. The latter is a nonlinear dissipative and driven quantum system that in the semiclassical limit displays typical bifurcations and chaotic behavior of the classical model. It is shown that the oscillator part of the qubits-oscillator system in the semiclassical limit is well described by the classical model despite the oscillator-qubit interaction. On the other hand, exact quantum dynamics of the qubits pair is completely different from the classical model as long as there is non-negligible qubit-oscillator interaction. Dynamics of the interqubits entanglement and the qubits pair von Neumann entropy is studied in the deeply quantum and various degrees of semiclassical regimes and for different values of the oscillator's bifurcation parameter. It is concluded that the decoherence of the qubits pair by the dissipative nonlinear oscillator is more effective when the oscillator is in the more classical regime, and if the semiclassical oscillator dynamics is chaotic rather than regular.

Physical Review A•Feb 2, 2009•10 citations

Classical dynamics of quantum entanglement

Giulio Casati, Italo Guarneri, Jose Reslen

We analyze numerically the dynamical generation of quantum entanglement in a system of two interacting particles, started in a coherent separable state, for decreasing values of ℏ. As ℏ→0 the entanglement entropy, computed at any finite time, converges to a finite nonzero value. The limit law that rules the time dependence of entropy is well reproduced by purely classical computations. Its general features can be explained by simple classical arguments, which expose the different ways entanglement is generated in systems that are classically chaotic or regular.

arXiv:1109.0907•Physical Review E•Mar 19, 2012•23 citations
We study the dynamical generation of entanglement for a very simple system: a pair of interacting spins, s1 and s2, in a constant magnetic field. Two different situations are considered:(a) s1 ->\infty, s2 = 1/2 and (b) s1 = s2 ->\infty, corresponding, respectively, to a quantum degree of freedom coupled to a semiclassical one (a qubit in contact with an environment) and a fully semiclassical system, which in this case displays chaotic behavior. Relations between quantum entanglement and classical dynamics are investigated.
We show how a classically vanishing interaction generates entanglement between two initially nonentangled particles, without affecting their classical dynamics. For chaotic dynamics, the rate of entanglement is shown to saturate at the Lyapunov exponent of the classical dynamics as the interaction strength increases. In the saturation regime, the one-particle Wigner function follows classical dynamics better and better as one goes deeper and deeper in the semiclassical limit. This demonstrates that quantum-classical correspondence at the microscopic level does not require coupling to a large number of external degrees of freedom.
Two particles, initially in a product state, become entangled when they come together and start to interact. Using semiclassical methods, we calculate the time evolution of the corresponding reduced density matrix rho(1), obtained by integrating out the degrees of freedom of one of the particles. We find that entanglement generation sensitively depends (i) on the interaction potential, especially on its strength and range, and (ii) on the nature of the underlying classical dynamics. Under general statistical assumptions, and for short-ranged interaction potentials, we find that P(t) decays exponentially fast in a chaotic environment, whereas it decays only algebraically in a regular system. In the chaotic case, the decay rate is given by the golden rule spreading of one-particle states due to the two-particle coupling, but cannot exceed the system's Lyapunov exponent.
We have studied the entanglement dynamics for a two-qubit system coupled to a spin environment of different configurations by a z–x-type interaction. Quantum dynamics of the models considered in this paper is solved analytically. Moreover, we show that simple and concise results may be obtained when certain approximations are properly made. Our purpose is to find out how the entanglement of a central spin system is affected by the pre-designed factors of the system and its environment, such as their initial states and the coupling constants between the system and its environment. Clearly, how the system is coupled to its environment will inevitably change the feature of entanglement evolution of the central spin system. Our major findings include the following: (i) the entanglement of the system of interest is sensitive to the number of spins in the environment, (ii) the initial states of the environment can profoundly affect the dynamics of the entanglement of the central spin system and (iii) the entangled environment can speed up the decay and revival of the entanglement of the central spin system. Our results exhibit some interesting features that have not been found for a bosonic environment.
We analyze the dynamical generation of entanglement in systems of two interacting spins initially prepared in a product of spin coherent states. For arbitrary time-independent Hamiltonians, we derive a semiclassical expression for the purity of the reduced density matrix as a function of time. The final formula, subsidiary to the linear entropy, shows that the short-time dynamics of entanglement depends exclusively on the stability of trajectories governed by the underlying classical Hamiltonian. In addition, this semiclassical measure is shown to reproduce the general properties of its quantum counterpart and give the expected result in the large spin limit. The accuracy of the semiclassical formula is further illustrated in a problem of phase exchange for two particles of spin jjj.
Quantum trajectories given by the quantum state diffusion theory are used to study the dynamics of a pair of qubits interacting with the quantized Duffing oscillator. The latter is a nonlinear dissipative and driven quantum system that in the semiclassical limit displays typical bifurcations and chaotic behavior of the classical model. It is shown that the oscillator part of the qubits-oscillator system in the semiclassical limit is well described by the classical model despite the oscillator-qubit interaction. On the other hand, exact quantum dynamics of the qubits pair is completely different from the classical model as long as there is non-negligible qubit-oscillator interaction. Dynamics of the interqubits entanglement and the qubits pair von Neumann entropy is studied in the deeply quantum and various degrees of semiclassical regimes and for different values of the oscillator's bifurcation parameter. It is concluded that the decoherence of the qubits pair by the dissipative nonlinear oscillator is more effective when the oscillator is in the more classical regime, and if the semiclassical oscillator dynamics is chaotic rather than regular.
We analyze numerically the dynamical generation of quantum entanglement in a system of two interacting particles, started in a coherent separable state, for decreasing values of ℏ. As ℏ→0 the entanglement entropy, computed at any finite time, converges to a finite nonzero value. The limit law that rules the time dependence of entropy is well reproduced by purely classical computations. Its general features can be explained by simple classical arguments, which expose the different ways entanglement is generated in systems that are classically chaotic or regular.