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Acta Physica Sinica

Dynamics of quantum correlation for three qubits in hierarchical environment

Yue Song, Jun‐Qi Li, Liang Jiu-Qing

Published Jan 1, 2021• 2 citations
Publisher

Abstract

Much attention has been paid to the dynamics of quantum correlation in an open quantum system coupled to a single-layered environment for a long time. However, the system can be influenced by the multilayer environment or hierarchical environment in realistic scenarios, which is attracting increasing interest at present. In this context, we explore in this paper the dynamics of quantum correlation for a quantum system consisting of three independent qubits, each being immersed in a single mode lossy cavity which is further connected to another cavity. The influences of cavity-cavity coupling strength Ω and the decay rate of cavity Γ1 on the measures of quantum correlation, including negativity, Bell non-locality as well as entanglement witness, are investigated in detail in a strong coupling regime and a weak coupling regime. It is shown that the phenomena of sudden death and sudden birth can happen to both Bell non-locality and entanglement witness. When the decay rate Γ1 = 0 is given, with the increase of Ω these measures eventually reach their stationary values over time after a short period of damping oscillations, in which these stationary values will become larger for the larger Ω. At the same time, the values or the survival times of quantum correlation considered by us in the weak coupling regime are better than in the strong coupling case. In addition, the non-zero Γ1 has a great negative effect on quantum correlation. Hence, in order to suppress the loss of quantum correlation better, the effective manipulation of quantum weak measurement and measurement reversal operator is considered further. Some interesting results are obtained.

DOI
10.7498/aps.70.20202133

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Much attention has been paid to the dynamics of quantum correlation in an open quantum system coupled to a single-layered environment for a long time. However, the system can be influenced by the multilayer environment or hierarchical environment in realistic scenarios, which is attracting increasing interest at present. In this context, we explore in this paper the dynamics of quantum correlation for a quantum system consisting of three independent qubits, each being immersed in a single mode lossy cavity which is further connected to another cavity. The influences of cavity-cavity coupling strength Ω and the decay rate of cavity Γ1 on the measures of quantum correlation, including negativity, Bell non-locality as well as entanglement witness, are investigated in detail in a strong coupling regime and a weak coupling regime. It is shown that the phenomena of sudden death and sudden birth can happen to both Bell non-locality and entanglement witness. When the decay rate Γ1 = 0 is given, with the increase of Ω these measures eventually reach their stationary values over time after a short period of damping oscillations, in which these stationary values will become larger for the larger Ω. At the same time, the values or the survival times of quantum correlation considered by us in the weak coupling regime are better than in the strong coupling case. In addition, the non-zero Γ1 has a great negative effect on quantum correlation. Hence, in order to suppress the loss of quantum correlation better, the effective manipulation of quantum weak measurement and measurement reversal operator is considered further. Some interesting results are obtained.
Quantum entanglement is one of most remarkable features of quantum mechanics,and in recent years it has played a more and more important role in quantum information.However,real quantum system inevitably interacts with the environment,resulting in the entanglement decay or even entanglement sudden death,so it is necessary to study the entanglement dynamical properties of an open system under different environments.In this paper,we investigate the entanglement dynamic behaviors of three interacting two-level atoms in an optical cavity which is coupled to a structured zero-temperature bosonic reservoir.Laplace transform,LBC and other methods are utilized,through numerical method we analyze the entanglement dynamic behavios of tripartite of three atoms and bipartite of cavity and reservoir.We also discuss how the coupling parameters affect the entanglement dynamics.Results show that in a short time,the entanglement of tripartite increases with coupling strength of three atoms increasing,and a periodic oscillation appears, but entanglement of bipartite decreases.The entanglement of tripartite decreases with the coupling strength between atoms and cavity increasing and damping oscillation appears,but the entanglement of bipartite increases.In a long-time limit,the entanglement approaches to a steady value.The non-Markovian dynamics of the qubits is determined by both the coupling strength and the spectral width.The strong system-reservoir coupling regime results in the non-Markovian dynamics of system.As the spectral width increases,the system of three atoms transforms from non-Markovian regime to Markovian regime.The increasing of spectral width results in the Markovian dynamic behavior of system,but the system of the atoms falls into the non-Markovian regime once more.When the coupling between the cavity and reservoir is weak,the entanglement of three atoms increases as the detuning of the cavity and reservoir increases,but it is not obvious.When the coupling between the cavity and reservoir is strong,the entanglement of three atoms increases and a periodic oscillation appears with increasing the detuning between the cavity and reservoir,so we can effectively restrain the effects of dissipation of reservoir on entanglement decay by adjusting the detuning between the cavity and reservoir.
Correlations in open quantum systems exhibit peculiar phenomena under the effect of various sources of noise. Here, we investigate the dynamics of entanglement and quantum discord (QD) for three noninteracting qubits coupled with a classical environmental static noise characterized by an external random field. Two initial entangled states of the system are examined, namely, the GHZ- and [Formula: see text]-type states. The system-environment interaction is here analyzed in three different configurations, namely, independent, mixed and common environments. We find that the dynamics of quantum correlations are strongly affected by the type of system-environment interaction and the purity of the initial entangled state. Indeed, depending on the type of interaction and the value of the purity of the initial state, peculiar phenomena such as sudden death, revivals and long-time survival of quantum correlations are observed. On the other hand, our results clearly show that quantum correlations initially present in the [Formula: see text]-type states are less robust than those of the GHZ-type states. Furthermore, we find that the long-time survival of entanglement can be detected by means of the suitable entanglement witnesses.
We study the dynamics of quantum dissension for three qubit states in various dissipative channels such as amplitude damping, dephasing and depolarizing. Our study is solely based on Markovian environments where quantum channels are without memory and each qubit is coupled to its own environment. We start with mixed GHZ, mixed W, mixture of separable states, a mixed biseparable state, as the initial states and mostly observe that the decay of quantum dissension is asymptotic in contrast to sudden death of quantum entanglement in similar environments. This is a clear indication of the fact that quantum correlation in general is more robust against the effect of noise. However, for a given class of initial mixed states we find a temporary leap in quantum dissension for a certain interval of time. More precisely, we observe the revival of quantum correlation to happen for certain time period. This signifies that the measure of quantum correlation such as quantum discord, quantum dissension, defined from the information theoretic perspective is different from the correlation defined from the entanglement-separability paradigm and can increase under the effect of the local noise. We also study the effects of these channels on the monogamy score of each of these initial states. Interestingly, we find that for certain class of states and channels, there is change from negative values to positive values of the monogamy score with classical randomness as well as with time. This gives us an important insight in obtaining states which are freely sharable (polygamous state) from the states which are not freely sharable (monogamous). This is indeed a remarkable feature, as we can create monogamous states from polygamous states Monogamous states are considered to have more signatures of quantum ness and can be used for security purpose.
Abstract Exploring strategies to protect quantum correlations from the detrimental effects of their surroundings is crucial in the field of quantum computing and information sciences. For this purpose, we consider a simple engineered environment consisting of two noninteracting separated qubits, each embedded in a single-mode lossy cavity which is further connected to another lossy cavity. We investigate the dynamics and protection of quantum discord for the initially maximum entangled state in the weak and strong coupling regimes between the qubits and their corresponding cavities. It is found that the quantum discord can be preserved efficiently for a much longer time by adjusting the hopping strengths between the two coupled cavities. In addition, if the secondary cavity is perfect then a stationary quantum discord between the two qubits arises after certain damping oscillations. Interestingly, the magnitude of the stationary quantum discord can be maximized by increasing the coupling strengths of the two cavities.
We have studied the dynamics of quantum correlations such as entanglement, Bell nonlocality and quantum discord between identical and unidentical atoms interacting with a single-mode cavity field and subject to cavity decay. The effect of single-atom detuning, cavity decay rate and initial preparation of the atoms on the corresponding correlation measures have been investigated. It is found that even under strong dissipation, time evolution can create high quantum discord while entanglement and Bell nonlocality stay zero for an initially separable state. Quantum discord increases while entanglement decreases in a certain time period under dissipation for the initial state that both atoms are in the excited state if the qubits are identical. For some types of initial states, cavity decay is shown to drive the system to a stationary state with high entanglement and quantum discord.
We investigate qubit entanglement dynamics in a two-qubit cavity system with stochastically fluctuating coupling strength, comparing white noise (Markovian) and Ornstein-Uhlenbeck noise (non-Markovian) processes. We analytically solve the system dynamics for both Fock and coherent cavity states and systematically characterize how initial qubit configurations affect entanglement generation and preservation. Our results reveal distinct dynamical regimes: in the Fock-state cavity, initial states in the single-excitation subspace generate robust qubit entanglement in decoherence-free subspaces, while initially entangled states in the double-excitation subspace exhibit inevitable decay without protective symmetries. For coherent cavities, we identify a critical photon-number threshold in the intermediate coherent-state amplitude regime where dynamics transition from low-frequency to high-frequency entanglement oscillations, while universal entanglement loss occurs at large amplitudes. Remarkable resilience against entanglement sudden death emerges under strong non-Markovian noise with long correlation times, where repeated revivals occur. These findings establish cavity photon statistics and environmental memory time as key control parameters for engineering qubit entanglement dynamics in qubit-cavity systems, revealing how system-environment correlations govern quantum information preservation.