© 2026 Aqora Quantum S.A.S.

Terms Privacy Legal Notice

arXiv:2411.13905 · Physical Review A

Transfer of nonlocality between two- and three-qubit dissipative systems with counter-rotating-wave terms

Zi-Yu Xiong, Yongjun Xiao, Ye-Qi Zhang, Qi-Liang He

Published Apr 7, 2025• 1 citation

Abstract

We investigate the effect of counter-rotating-wave terms on nonlocality and entanglement for three qubits coupled to a common bath for strong- and ultrastrong-coupling regimes beyond the traditional treatment of Born-Markovian, perturbative, and rotating-wave approximations by employing the numerical hierarchical equations-of-motion approach. Our findings are as follows: (1) In the strong-coupling regime, the counter-rotating terms accelerate the decay of genuine three-party correlations, and the obvious sudden birth of Bell nonlocality is found. (2) In the ultrastrong-coupling regime, we observe a phenomenon in which nonlocality is consistently transferred between a three-qubit system and its subsystem. In addition, the inclusion of counter-rotating wave terms obviously enhances genuine tripartite nonlocality. (3) These counter-rotating terms cannot effectively generate genuine three-party correlations in zero-excitation cases, which differs from previous studies involving only two qubits. (4) A significant reduction in steady-state correlations for three- and two-party systems due to counter-rotating-wave terms is observed, which is not detectable under the rotating-wave approximation.

DOI: 10.1103/physreva.111.042410

Related papers

Decoherence of two qubits in non-Markovian reservoirs without the rotating-wave approximation

Wang Fa-Qiang, Zhi‐Ming Zhang, Ruisheng Liang

The decoherence of two initially entangled qubits in non-Markovian reservoirs has been investigated exactly without Born-Markovian approximation or rotating-wave approximation (RWA). The nonperturbative quantum master equation is derived and its exact solution is obtained. The decoherence behavior of two qubits, initially entangled in Bell states, has been investigated in the weak coupling regime and strong coupling regime. The results show that the counter-rotating wave terms have obvious influence on the decoherence behavior in the non-Markovian regime.

arXiv:0806.3306•Physical Review A•Dec 9, 2008•24 citations

Exact dynamics of quantum correlations of two qubits coupled to bosonic baths

Chen Wang, Qing-Hu Chen

Dynamics of the quantum entanglement and quantum discord of two qubits in two independent baths and a common bath with the Lorentzian spectrum are studied exactly in the numerical sense within the hierarchy approach. The effects of the counter-rotating-wave terms from the system–bath coherence on these quantum correlations are systematically discussed and comparisons with previous ones under the rotating-wave approximation are also performed. For two independent baths, beyond the weak system–bath coupling, the counter-rotating-wave terms essentially change evolutions of both the entanglement and quantum discord. With increase of the coupling, revival of the entanglement after a period of complete disentanglement is suppressed dramatically and finally disappears, and the quantum discord becomes smaller monotonically. For the common bath, the entanglement is also suppressed by the counter-rotating-wave terms, but the quantum discord shows quite different behaviors if initiated from spin-correlated states. In the non-Markovian regime, the quantum discord is almost not influenced by the counter-rotating-wave terms and is generally finite in the long-time evolution at arbitrary coupling while in the Markovian regime, it is significantly enhanced with the strong coupling.

arXiv:1303.1054•New Journal of Physics•Oct 17, 2013•46 citations

Entanglement dynamics of two qubits in a common bath

Jian Ma, Zhe Sun, Xiaoguang Wang +1 more

We derive a set of hierarchical equations for qubits interacting with a Lorentz-broadened cavity mode at zero temperature, without using the rotating-wave, Born, and Markovian approximations. We use this exact method to reexamine the entanglement dynamics of two qubits interacting with a common bath, which was previously solved only under the rotating-wave and single-excitation approximations. With the exact hierarchy equation method used here, double excitations due to counter-rotating-wave terms are found to have remarkable effects on the dynamics and the steady-state entanglement.

arXiv:1202.0688•Physical Review A•Jun 26, 2012•158 citations

Entanglement evolution of a two-qubit system with decay beyond the rotating-wave approximation

杨青, Yang Ming, 李大创 +1 more

The entanglement property of two identical atoms, initially entangled in Bell states, coupled to a single-mode cavity is considered. Based on the reduced non-perturbative quantum master equation method, the entanglement evolution of the two atoms with decay is investigated beyond the conventional rotating-wave approximation. We show that the counter-rotating wave terms, usually neglected, have a great influence on the disentanglement behaviour of the system. The phenomena of entanglement sudden death and entanglement sudden birth will occur. In addition, we show that the entanglement can be strengthened by introducing the dipole-dipole interaction of the two atoms.

Chinese Physics B•Nov 1, 2009•3 citations

Impact of counter-rotating-wave term on quantum heat transfer and phonon statistics in nonequilibrium qubit–phonon hybrid system*

Chen Wang, Lu-Qin Wang, Jie Ren

Counter-rotating-wave terms (CRWTs) are traditionally viewed to be crucial in open small quantum systems with strong system–bath dissipation. Here by exemplifying in a nonequilibrium qubit–phonon hybrid model, we show that CRWTs can play the significant role in quantum heat transfer even with weak system–bath dissipation. By using extended coherent phonon states, we obtain the quantum master equation with heat exchange rates contributed by rotating-wave-terms (RWTs) and CRWTs, respectively. We find that including only RWTs, the steady state heat current and current fluctuations will be significantly suppressed at large temperature bias, whereas they are strongly enhanced by considering CRWTs in addition. Furthermore, for the phonon statistics, the average phonon number and two-phonon correlation are nearly insensitive to strong qubit–phonon hybridization with only RWTs, whereas they will be dramatically cooled down via the cooperative transitions based on CRWTs in addition. Therefore, CRWTs in quantum heat transfer system should be treated carefully.

arXiv:2010.04026•Chinese Physics B•Dec 2, 2020•6 citations

Effects of counter-rotating-wave terms on the non-Markovianity in quantum open systems

Wei Wu, Maoxin Liu

We investigate the effect of counter-rotating-wave terms on the non-Markovianity in quantum open systems by employing the hierarchical equations of motion in the framework of the non-Markovian quantum state diffusion approach. As illustrative examples, the non-Markovian memory effect of a qubit embedded in a bosonic or a fermionic environment with a detuned Lorentz spectrum at zero temperature is analyzed. It is found that the counter-rotating-wave terms are able to enhance the observed non-Markovianity whether the environment is composed of bosons or fermions. This result suggests that the rotating-wave approximation may reduce the non-Markovianity in quantum open systems. Moreover, we find that the modification of the non-Markovianity due to the different statistical properties of environmental modes becomes larger with the increase of the system-environment coupling strength.

arXiv:1706.09576•Physical Review A•Sep 29, 2017•18 citations

We investigate the effect of counter-rotating-wave terms on nonlocality and entanglement for three qubits coupled to a common bath for strong- and ultrastrong-coupling regimes beyond the traditional treatment of Born-Markovian, perturbative, and rotating-wave approximations by employing the numerical hierarchical equations-of-motion approach. Our findings are as follows: (1) In the strong-coupling regime, the counter-rotating terms accelerate the decay of genuine three-party correlations, and the obvious sudden birth of Bell nonlocality is found. (2) In the ultrastrong-coupling regime, we observe a phenomenon in which nonlocality is consistently transferred between a three-qubit system and its subsystem. In addition, the inclusion of counter-rotating wave terms obviously enhances genuine tripartite nonlocality. (3) These counter-rotating terms cannot effectively generate genuine three-party correlations in zero-excitation cases, which differs from previous studies involving only two qubits. (4) A significant reduction in steady-state correlations for three- and two-party systems due to counter-rotating-wave terms is observed, which is not detectable under the rotating-wave approximation.

The decoherence of two initially entangled qubits in non-Markovian reservoirs has been investigated exactly without Born-Markovian approximation or rotating-wave approximation (RWA). The nonperturbative quantum master equation is derived and its exact solution is obtained. The decoherence behavior of two qubits, initially entangled in Bell states, has been investigated in the weak coupling regime and strong coupling regime. The results show that the counter-rotating wave terms have obvious influence on the decoherence behavior in the non-Markovian regime.

Dynamics of the quantum entanglement and quantum discord of two qubits in two independent baths and a common bath with the Lorentzian spectrum are studied exactly in the numerical sense within the hierarchy approach. The effects of the counter-rotating-wave terms from the system–bath coherence on these quantum correlations are systematically discussed and comparisons with previous ones under the rotating-wave approximation are also performed. For two independent baths, beyond the weak system–bath coupling, the counter-rotating-wave terms essentially change evolutions of both the entanglement and quantum discord. With increase of the coupling, revival of the entanglement after a period of complete disentanglement is suppressed dramatically and finally disappears, and the quantum discord becomes smaller monotonically. For the common bath, the entanglement is also suppressed by the counter-rotating-wave terms, but the quantum discord shows quite different behaviors if initiated from spin-correlated states. In the non-Markovian regime, the quantum discord is almost not influenced by the counter-rotating-wave terms and is generally finite in the long-time evolution at arbitrary coupling while in the Markovian regime, it is significantly enhanced with the strong coupling.

We derive a set of hierarchical equations for qubits interacting with a Lorentz-broadened cavity mode at zero temperature, without using the rotating-wave, Born, and Markovian approximations. We use this exact method to reexamine the entanglement dynamics of two qubits interacting with a common bath, which was previously solved only under the rotating-wave and single-excitation approximations. With the exact hierarchy equation method used here, double excitations due to counter-rotating-wave terms are found to have remarkable effects on the dynamics and the steady-state entanglement.

The entanglement property of two identical atoms, initially entangled in Bell states, coupled to a single-mode cavity is considered. Based on the reduced non-perturbative quantum master equation method, the entanglement evolution of the two atoms with decay is investigated beyond the conventional rotating-wave approximation. We show that the counter-rotating wave terms, usually neglected, have a great influence on the disentanglement behaviour of the system. The phenomena of entanglement sudden death and entanglement sudden birth will occur. In addition, we show that the entanglement can be strengthened by introducing the dipole-dipole interaction of the two atoms.

Counter-rotating-wave terms (CRWTs) are traditionally viewed to be crucial in open small quantum systems with strong system–bath dissipation. Here by exemplifying in a nonequilibrium qubit–phonon hybrid model, we show that CRWTs can play the significant role in quantum heat transfer even with weak system–bath dissipation. By using extended coherent phonon states, we obtain the quantum master equation with heat exchange rates contributed by rotating-wave-terms (RWTs) and CRWTs, respectively. We find that including only RWTs, the steady state heat current and current fluctuations will be significantly suppressed at large temperature bias, whereas they are strongly enhanced by considering CRWTs in addition. Furthermore, for the phonon statistics, the average phonon number and two-phonon correlation are nearly insensitive to strong qubit–phonon hybridization with only RWTs, whereas they will be dramatically cooled down via the cooperative transitions based on CRWTs in addition. Therefore, CRWTs in quantum heat transfer system should be treated carefully.

We investigate the effect of counter-rotating-wave terms on the non-Markovianity in quantum open systems by employing the hierarchical equations of motion in the framework of the non-Markovian quantum state diffusion approach. As illustrative examples, the non-Markovian memory effect of a qubit embedded in a bosonic or a fermionic environment with a detuned Lorentz spectrum at zero temperature is analyzed. It is found that the counter-rotating-wave terms are able to enhance the observed non-Markovianity whether the environment is composed of bosons or fermions. This result suggests that the rotating-wave approximation may reduce the non-Markovianity in quantum open systems. Moreover, we find that the modification of the non-Markovianity due to the different statistical properties of environmental modes becomes larger with the increase of the system-environment coupling strength.