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:1302.5231 · Physical Review A

Fading entanglement near an equilibrium state

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

Published Sep 26, 2012• 6 citations
arXivHTMLPDF

Abstract

It was recently shown that entanglement in quantum systems being in a nonequilibrium state can appear at much higher temperatures than in an equilibrium state. However, any system is subject to the natural relaxation process establishing equilibrium. The work deals with the numerical study of entanglement dynamics in a dipolar coupled spin-1/2 system under the transition from a nonequilibrium state to an equilibrium state. The spin system is characterized by a two-temperature density matrix, and the process of the establishment of equilibrium is in the equalization of these temperatures. The method of the nonequilibrium statistical operator is used to describe the evolution of the system. The process of establishing an equilibrium state in the homonuclear spin systems at low temperature was first considered. It was shown that the time dependencies of the inverse temperatures of the spin subsystems are given by a solution of nonlinear equations in contrast to the linear equations in the well-known high-temperature approximation. We have first studied the entanglement dynamics during the equilibrium state establishment and have found that the concurrence changes nonmonotonically with time and temperatures while equilibrium is being established. Entanglement fades long before equilibrium is established in the system. It was shown that the entanglement dynamics depends strongly on the ratio of the Zeeman energy to the dipolar energy. At a high ratio, the concurrence in the system decreases quickly for a time of about 100 $\ensuremath{\mu}\text{s}$ whereas, at a low ratio, establishment of equilibrium and fading entanglement takes a prolonged time up to 1 $\text{ms}$.

DOI
10.1103/physreva.86.032336

Related papers

Nonequilibrium thermal entanglement for simple qubit systems

Ilya Sinayskiy, N. Pumulo, Francesco Petruccione

The dynamics of simple qubit systems in a chain configuration coupled at both ends to separate bosonic baths at different temperatures is studied. An exact analytical solution of the master equation in the Born-Markov approximation for the reduced density matrix of the qubit system is constructed. The unique non-equilibrium stationary state for the long time behavior of the reduced density matrix in obtained. Dynamical and steady state properties of the concurrence between the first and the last spin are studied.

arXiv:1401.2306•Jan 10, 2014•0 citations

Dynamics of nonequilibrium thermal entanglement

Ilya Sinayskiy, Francesco Petruccione, Daniel Klaus Burgarth

The dynamics of a simple spin chain (two spins) coupled to bosonic baths at different temperatures is studied. The analytical solution for the reduced density matrix of the system is found. The dynamics and temperature dependence of spin-spin entanglement is analyzed. It is shown that the system converges to a steady state. If the energy levels of the two spins are different, the steady-state concurrence assumes its maximum at unequal bath temperatures. It is found that a difference in local energy levels can make the steady-state entanglement more stable against high temperatures.

arXiv:0807.0379•Physical Review A•Dec 2, 2008•78 citations

Quantum Entanglement in Quasi-Equilibrium States in the Multipulse Spin Locking of the Nuclear Magnetic Resonance

G. A. Bochkin, Sergey G. Vasil’ev, E. I. Kuznetsova +1 more

Quantum entanglement is studied NMR multipulse spin locking, when a system of spins coupled by the dipole–dipole interaction in a strong magnetic field is irradiated by a sequence of resonant high-frequency $$\varphi $$ -pulses with the same time delay $$2\tau $$ between successive pulses. For times $$t \sim {{T}_{2}}$$ ( $${{T}_{2}} \approx \omega _{{{\text{loc}}}}^{{ - 1}}$$ , $${{\omega }_{{{\text{loc}}}}}$$ is determined by the dipole–dipole interaction), quasi-equilibrium with a structure depending on the relation between the pulsed field $${{\omega }_{1}} = \varphi {\text{/}}2\tau $$ and $${{\omega }_{{{\text{loc}}}}}$$ is established in the system. For $${{\omega }_{1}} \lessapprox {{\omega }_{{{\text{loc}}}}}$$ , a one-temperature quasi-equilibrium state arises, while a quasi-equilibrium with the dipole and Zeeman temperatures appears for $${{\omega }_{1}} \gg {{\omega }_{{{\text{loc}}}}}$$ . The temperature dependence of entanglement is investigated for $${{\omega }_{1}} \lessapprox {{\omega }_{{{\text{loc}}}}}$$ . For $${{\omega }_{1}} \gg {{\omega }_{{{\text{loc}}}}}$$ , the further evolution of the system is determined by the Provotorov equations and leads to the equalization of the dipole and Zeeman temperatures. It is shown that the entanglement is absent in this case.

Journal of Experimental and Theoretical Physics Letters•Apr 1, 2025•1 citation

Quantum entanglement at negative temperature

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

An isolated spin system that is in internal thermodynamic equilibrium and that has an upper limit to its allowed energy states can possess a negative temperature. We calculate the thermodynamic characteristics and the concurrence in this system over the entire range of positive and negative temperatures. Our calculation was performed for different real structures, which can be used in experiments. It is found that the temperature dependence of the concurrence is substantially asymmetrical similarly to other thermodynamic characteristics. At a negative temperature the maximum concurrence and the absolute temperature of the entanglement appearance are significantly larger than those at a positive temperature. The concurrence can be characterized by two dimensionless parameters: the ratio between the Zeeman and dipolar energies and the ratio of the thermal and dipolar energies. It was shown that for all considered structures the dimensionless temperatures of the transition between entanglement and separability of the first and second spins are independent of spin structure and the number of spins.

arXiv:1302.5232•Journal of Physics A Mathematical and Theoretical•Mar 13, 2013•5 citations

Nonequilibrium thermal entanglement for simple spin chains

Ilya Sinayskiy, N. Pumulo, Francesco Petruccione

The dynamics of a chain of two and three spins coupled at both ends to separate bosonic baths at different temperatures is studied. An exact analytical solution of the quantum master equation in the Born-Markov approximation for the reduced density matrix of the chain is constructed. It is shown that for long times the reduced density matrix converges to the nonequilibrium steady-state. Dynamical and steady state properties of the concurrence between the first and the last spin are studied.

AIP conference proceedings•Jan 1, 2012•0 citations

Quantum entanglement at high temperatures? Bosonic systems in nonequilibrium steady state

Jen-Tsung Hsiang, B. L. Hu

This is the second of a series of three papers examining how viable it is for entanglement to be sustained at high temperatures for quantum systems in thermal equilibrium (Case A), in nonequilibrium (Case B) and in nonequilibrium steady state (NESS) conditions (Case C). The system we analyze here consists of two coupled quantum harmonic oscillators each interacting with its own bath described by a scalar field, set at temperatures T 1 > T 2. For constant bilinear inter-oscillator coupling studied here (Case C1) owing to the Gaussian nature, the problem can be solved exactly at arbitrary temperatures even for strong coupling. We find that the valid entanglement criterion in general is not a function of the bath temperature difference, in contrast to thermal transport in the same NESS setting [1]. Thus lowering the temperature of one of the thermal baths does not necessarily help to safeguard the entanglement between the oscillators. Indeed, quantum entanglement will disappear if any one of the thermal baths has a temperature higher than the critical temperature T c, defined as the temperature above which quantum entanglement vanishes. With the Langevin equations derived we give a full display of how entanglement dynamics in this system depends on T 1, T 2, the inter-oscillator coupling and the system-bath coupling strengths. For weak oscillator-bath coupling the critical temperature T c is about the order of the inverse oscillator frequency, but for strong oscillator-bath coupling it will depend on the bath cutoff frequency. We conclude that in most realistic circumstances, for bosonic systems in NESS with constant bilinear coupling, ‘hot entanglement’ is largely a fiction.

arXiv:1503.03587•Journal of High Energy Physics•Nov 1, 2015•17 citations
It was recently shown that entanglement in quantum systems being in a nonequilibrium state can appear at much higher temperatures than in an equilibrium state. However, any system is subject to the natural relaxation process establishing equilibrium. The work deals with the numerical study of entanglement dynamics in a dipolar coupled spin-1/2 system under the transition from a nonequilibrium state to an equilibrium state. The spin system is characterized by a two-temperature density matrix, and the process of the establishment of equilibrium is in the equalization of these temperatures. The method of the nonequilibrium statistical operator is used to describe the evolution of the system. The process of establishing an equilibrium state in the homonuclear spin systems at low temperature was first considered. It was shown that the time dependencies of the inverse temperatures of the spin subsystems are given by a solution of nonlinear equations in contrast to the linear equations in the well-known high-temperature approximation. We have first studied the entanglement dynamics during the equilibrium state establishment and have found that the concurrence changes nonmonotonically with time and temperatures while equilibrium is being established. Entanglement fades long before equilibrium is established in the system. It was shown that the entanglement dynamics depends strongly on the ratio of the Zeeman energy to the dipolar energy. At a high ratio, the concurrence in the system decreases quickly for a time of about 100 \ensuremathμs\ensuremath{\mu}\text{s}\ensuremathμs whereas, at a low ratio, establishment of equilibrium and fading entanglement takes a prolonged time up to 1 ms\text{ms}ms.
The dynamics of simple qubit systems in a chain configuration coupled at both ends to separate bosonic baths at different temperatures is studied. An exact analytical solution of the master equation in the Born-Markov approximation for the reduced density matrix of the qubit system is constructed. The unique non-equilibrium stationary state for the long time behavior of the reduced density matrix in obtained. Dynamical and steady state properties of the concurrence between the first and the last spin are studied.
The dynamics of a simple spin chain (two spins) coupled to bosonic baths at different temperatures is studied. The analytical solution for the reduced density matrix of the system is found. The dynamics and temperature dependence of spin-spin entanglement is analyzed. It is shown that the system converges to a steady state. If the energy levels of the two spins are different, the steady-state concurrence assumes its maximum at unequal bath temperatures. It is found that a difference in local energy levels can make the steady-state entanglement more stable against high temperatures.
Quantum entanglement is studied NMR multipulse spin locking, when a system of spins coupled by the dipole–dipole interaction in a strong magnetic field is irradiated by a sequence of resonant high-frequency φ\varphi φ -pulses with the same time delay 2τ2\tau 2τ between successive pulses. For times t∼T2t \sim {{T}_{2}}t∼T2​ ( T2≈ωloc−1{{T}_{2}} \approx \omega _{{{\text{loc}}}}^{{ - 1}}T2​≈ωloc−1​ , ωloc{{\omega }_{{{\text{loc}}}}}ωloc​ is determined by the dipole–dipole interaction), quasi-equilibrium with a structure depending on the relation between the pulsed field ω1=φ/2τ{{\omega }_{1}} = \varphi {\text{/}}2\tau ω1​=φ/2τ and ωloc{{\omega }_{{{\text{loc}}}}}ωloc​ is established in the system. For ω1⪅ωloc{{\omega }_{1}} \lessapprox {{\omega }_{{{\text{loc}}}}}ω1​⪅ωloc​ , a one-temperature quasi-equilibrium state arises, while a quasi-equilibrium with the dipole and Zeeman temperatures appears for ω1≫ωloc{{\omega }_{1}} \gg {{\omega }_{{{\text{loc}}}}}ω1​≫ωloc​ . The temperature dependence of entanglement is investigated for ω1⪅ωloc{{\omega }_{1}} \lessapprox {{\omega }_{{{\text{loc}}}}}ω1​⪅ωloc​ . For ω1≫ωloc{{\omega }_{1}} \gg {{\omega }_{{{\text{loc}}}}}ω1​≫ωloc​ , the further evolution of the system is determined by the Provotorov equations and leads to the equalization of the dipole and Zeeman temperatures. It is shown that the entanglement is absent in this case.
An isolated spin system that is in internal thermodynamic equilibrium and that has an upper limit to its allowed energy states can possess a negative temperature. We calculate the thermodynamic characteristics and the concurrence in this system over the entire range of positive and negative temperatures. Our calculation was performed for different real structures, which can be used in experiments. It is found that the temperature dependence of the concurrence is substantially asymmetrical similarly to other thermodynamic characteristics. At a negative temperature the maximum concurrence and the absolute temperature of the entanglement appearance are significantly larger than those at a positive temperature. The concurrence can be characterized by two dimensionless parameters: the ratio between the Zeeman and dipolar energies and the ratio of the thermal and dipolar energies. It was shown that for all considered structures the dimensionless temperatures of the transition between entanglement and separability of the first and second spins are independent of spin structure and the number of spins.
This is the second of a series of three papers examining how viable it is for entanglement to be sustained at high temperatures for quantum systems in thermal equilibrium (Case A), in nonequilibrium (Case B) and in nonequilibrium steady state (NESS) conditions (Case C). The system we analyze here consists of two coupled quantum harmonic oscillators each interacting with its own bath described by a scalar field, set at temperatures T 1 > T 2. For constant bilinear inter-oscillator coupling studied here (Case C1) owing to the Gaussian nature, the problem can be solved exactly at arbitrary temperatures even for strong coupling. We find that the valid entanglement criterion in general is not a function of the bath temperature difference, in contrast to thermal transport in the same NESS setting [1]. Thus lowering the temperature of one of the thermal baths does not necessarily help to safeguard the entanglement between the oscillators. Indeed, quantum entanglement will disappear if any one of the thermal baths has a temperature higher than the critical temperature T c, defined as the temperature above which quantum entanglement vanishes. With the Langevin equations derived we give a full display of how entanglement dynamics in this system depends on T 1, T 2, the inter-oscillator coupling and the system-bath coupling strengths. For weak oscillator-bath coupling the critical temperature T c is about the order of the inverse oscillator frequency, but for strong oscillator-bath coupling it will depend on the bath cutoff frequency. We conclude that in most realistic circumstances, for bosonic systems in NESS with constant bilinear coupling, ‘hot entanglement’ is largely a fiction.