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:2409.16244 · Physica Scripta

Unique entanglement time evolution of two-qubit product separable and extended Werner-like states in a discrete qubit environment

Renzo P. Alporha, Lemuel John F. Sese, Rayda Gammag

Published Jul 10, 2025• 0 citations
arXivHTMLPDF

Abstract

Abstract This study investigates the parameters affecting the entanglement time evolution of product separable (PS) and extended Werner-like (EWL) states in homogeneous, white noise, and mixed environments. In a pure homogeneous environment, both states demonstrate complete entanglement revivals, where an increase in the number of environments leads to an attenuation of concurrence. The PS state exhibits gaps and never reaches a maximum entanglement, whereas maximum purity EWL states (Bell states) maintain or periodically reach maximum entanglement. Hence, the PS and EWL states have a disjoint entanglement time evolution subspaces. Interestingly, the environment interaction and subsystem coupling interaction that influence entanglement have an inverse time relationship under a constant value of concurrence. Placing the system of interest in a white noise environment induces entanglement dissipation, with the dissipation time dependent on the width of random distribution of interaction strengths rather than the magnitude of interaction strength. In a distinct qubit environment, the entanglement time evolution of the PS state depends on the distribution of the number of environments. Moreover, combining homogeneous and white noise environments results in entanglement dynamics that exhibit characteristics of both homogeneous and white noise.

DOI
10.1088/1402-4896/adedc7

Related papers

Disentanglement Dynamics in Nonequilibrium Environments

Mingli Chen, Haonan Chen, Tao Han +1 more

We theoretically study the non-Markovian disentanglement dynamics of a two-qubit system coupled to nonequilibrium environments with nonstationary and non-Markovian random telegraph noise statistical properties. The reduced density matrix of the two-qubit system can be expressed as the Kraus representation in terms of the tensor products of the single qubit Kraus operators. We derive the relation between the entanglement and nonlocality of the two-qubit system which are both closely associated with the decoherence function. We identify the threshold values of the decoherence function to ensure the existences of the concurrence and nonlocal quantum correlations for an arbitrary evolution time when the two-qubit system is initially prepared in the composite Bell states and the Werner states, respectively. It is shown that the environmental nonequilibrium feature can suppress the disentanglement dynamics and reduce the entanglement revivals in non-Markovian dynamics regime. In addition, the environmental nonequilibrium feature can enhance the nonlocality of the two-qubit system. Moreover, the entanglement sudden death and rebirth phenomena and the transition between quantum and classical nonlocalities closely depend on the parameters of the initial states and the environmental parameters in nonequilibrium environments.

Entropy•Sep 21, 2022•9 citations

Sudden birth versus sudden death of entanglement for the extended Werner-like state in a dissipative environment

Shan Chuan-Jia, Tao Chen, Ji-Bing Liu +4 more

In this paper, we investigate the dynamical behaviour of entanglement in terms of concurrence in a bipartite system subjected to an external magnetic field under the action of dissipative environments in the extended Werner-like initial state. The interesting phenomenon of entanglement sudden death as well as sudden birth appears during the evolution process. We analyse in detail the effect of the purity of the initial entangled state of two qubits via Heisenberg XY interaction on the apparition time of entanglement sudden death and entanglement sudden birth. Furthermore, the conditions on the conversion of entanglement sudden death and entanglement sudden birth can be generalized when the initial entangled state is not pure. In particular, a critical purity of the initial mixed entangled state exists, above which entanglement sudden birth vanishes while entanglement sudden death appears. It is also noticed that stable entanglement, which is independent of different initial states of the qubits (pure or mixed state), occurs even in the presence of decoherence. These results arising from the combination of the extended Werner-like initial state and dissipative environments suggest an approach to control and enhance the entanglement even after purity induced sudden birth, death and revival.

Chinese Physics B•Jun 1, 2010•7 citations

Relation between initial conditions and entanglement sudden death for two-qubit extended Werner-like states

Baiyuan Yang, Mao-Fa Fang, Jiang Huang

In this paper, the dynamical behavior of entanglement of an uncoupled two-qubit system, which interacts with independent identical amplitude damping environments and is initially prepared in the extended Werner-like (EWL) states, is investigated. The results show that whether entanglement sudden death (ESD) of an EWL state will occur or not depends on initial purity and concurrence. The boundaries between ESD states and ESD-free states for two kinds of EWL states are found to be different. Furthermore, some regions are shown where ESD states can be transformed into ESD-free states by local unitary operations.

Chinese Physics B•Aug 1, 2013•4 citations

Entanglement for Two-Qubit Extended Werner-Like States: Effect of Non-Markovian Environments

Shan Chuan-Jia, Ji-Bing Liu, Tao Chen +4 more

We investigate the sudden birth and sudden death of entanglement of two qubits interacting with un-correlated structured reservoirs. The system is initially prepared in two-qubit extended Werner-like state. We work out the dependence of the entanglement dynamics on both non-Markovian environments and the purity of initial state, and show that non-Markovian environments and the purity can control the time of the two-qubit entanglement sudden death and the reservoirs' entanglement sudden birth. Furthermore, under the conditions of different purity and initial entanglement, the revival of qubits' entanglement can manifest before, simultaneously or even after the disentanglement of their corresponding reservoirs.

Communications in Theoretical Physics•Sep 1, 2010•3 citations

Dynamical concurrence of initially separable bipartite system immersed in N-qubit environment

Renzo P. Alporha, Lemuel John F. Sese, Rayda Gammag

Abstract In this paper, we calculate the concurrence for two entangled qubits that are immersed in either a homogeneous or a heterogeneous N-qubit environment. The concurrence for the discrete homogeneous environment was found to behave periodically depending on the interaction strengths ω S 1 S 2 and Γ. For the case of a heterogeneous environment, we set the interaction strength Γ Siεk as uniformly random. This case mimics of a noisy environment as it illustrates an asymptotic decay of entanglement. The sudden death behavior found in the heterogenous case becomes more prominent for larger N number of qubit environments, and no other entanglement is found as time t → ∞.

Journal of Physics Conference Series•Jul 1, 2024•1 citation

Entanglement Degradation in Two Interacting Qubits Coupled to Dephasing Environments

Rahma Abdelmagid, Khadija Alshehhi, Gehad Sadiek

One of the main obstacles toward building efficient quantum computing systems is decoherence, where the inevitable interaction between the qubits and the surrounding environment leads to a vanishing entanglement. We consider a system of two interacting asymmetric two-level atoms (qubits) in the presence of pure and correlated dephasing environments. We study the dynamics of entanglement while varying the interaction strength between the two qubits, their relative frequencies, and their coupling strength to the environment starting from different initial states of practical interest. The impact of the asymmetry of the two qubits, reflected in their different frequencies and coupling strengths to the environment, varies significantly depending on the initial state of the system and its degree of anisotropy. For an initial disentangled, or a Werner, state, as the difference between the frequencies increases, the entanglement decay rate increases, with more persistence at the higher degrees of anisotropy in the former state. However, for an initial anti-correlated Bell state, the entanglement decays more rapidly in the symmetric case compared with the asymmetric one. The difference in the coupling strengths of the two qubits to the pure (uncorrelated) dephasing environment leads to higher entanglement decay in the different initial state cases, though the rate varies depending on the degree of anisotropy and the initial state. Interestingly, the correlated dephasing environment, within a certain range, was found to enhance the entanglement dynamics starting from certain initial states, such as the disentangled, anti-correlated Bell, and Werner, whereas it exhibits a decaying effect in other cases such as the initial correlated Bell state.

Entropy•Oct 17, 2023•5 citations
Abstract This study investigates the parameters affecting the entanglement time evolution of product separable (PS) and extended Werner-like (EWL) states in homogeneous, white noise, and mixed environments. In a pure homogeneous environment, both states demonstrate complete entanglement revivals, where an increase in the number of environments leads to an attenuation of concurrence. The PS state exhibits gaps and never reaches a maximum entanglement, whereas maximum purity EWL states (Bell states) maintain or periodically reach maximum entanglement. Hence, the PS and EWL states have a disjoint entanglement time evolution subspaces. Interestingly, the environment interaction and subsystem coupling interaction that influence entanglement have an inverse time relationship under a constant value of concurrence. Placing the system of interest in a white noise environment induces entanglement dissipation, with the dissipation time dependent on the width of random distribution of interaction strengths rather than the magnitude of interaction strength. In a distinct qubit environment, the entanglement time evolution of the PS state depends on the distribution of the number of environments. Moreover, combining homogeneous and white noise environments results in entanglement dynamics that exhibit characteristics of both homogeneous and white noise.
We theoretically study the non-Markovian disentanglement dynamics of a two-qubit system coupled to nonequilibrium environments with nonstationary and non-Markovian random telegraph noise statistical properties. The reduced density matrix of the two-qubit system can be expressed as the Kraus representation in terms of the tensor products of the single qubit Kraus operators. We derive the relation between the entanglement and nonlocality of the two-qubit system which are both closely associated with the decoherence function. We identify the threshold values of the decoherence function to ensure the existences of the concurrence and nonlocal quantum correlations for an arbitrary evolution time when the two-qubit system is initially prepared in the composite Bell states and the Werner states, respectively. It is shown that the environmental nonequilibrium feature can suppress the disentanglement dynamics and reduce the entanglement revivals in non-Markovian dynamics regime. In addition, the environmental nonequilibrium feature can enhance the nonlocality of the two-qubit system. Moreover, the entanglement sudden death and rebirth phenomena and the transition between quantum and classical nonlocalities closely depend on the parameters of the initial states and the environmental parameters in nonequilibrium environments.
In this paper, we investigate the dynamical behaviour of entanglement in terms of concurrence in a bipartite system subjected to an external magnetic field under the action of dissipative environments in the extended Werner-like initial state. The interesting phenomenon of entanglement sudden death as well as sudden birth appears during the evolution process. We analyse in detail the effect of the purity of the initial entangled state of two qubits via Heisenberg XY interaction on the apparition time of entanglement sudden death and entanglement sudden birth. Furthermore, the conditions on the conversion of entanglement sudden death and entanglement sudden birth can be generalized when the initial entangled state is not pure. In particular, a critical purity of the initial mixed entangled state exists, above which entanglement sudden birth vanishes while entanglement sudden death appears. It is also noticed that stable entanglement, which is independent of different initial states of the qubits (pure or mixed state), occurs even in the presence of decoherence. These results arising from the combination of the extended Werner-like initial state and dissipative environments suggest an approach to control and enhance the entanglement even after purity induced sudden birth, death and revival.
In this paper, the dynamical behavior of entanglement of an uncoupled two-qubit system, which interacts with independent identical amplitude damping environments and is initially prepared in the extended Werner-like (EWL) states, is investigated. The results show that whether entanglement sudden death (ESD) of an EWL state will occur or not depends on initial purity and concurrence. The boundaries between ESD states and ESD-free states for two kinds of EWL states are found to be different. Furthermore, some regions are shown where ESD states can be transformed into ESD-free states by local unitary operations.
We investigate the sudden birth and sudden death of entanglement of two qubits interacting with un-correlated structured reservoirs. The system is initially prepared in two-qubit extended Werner-like state. We work out the dependence of the entanglement dynamics on both non-Markovian environments and the purity of initial state, and show that non-Markovian environments and the purity can control the time of the two-qubit entanglement sudden death and the reservoirs' entanglement sudden birth. Furthermore, under the conditions of different purity and initial entanglement, the revival of qubits' entanglement can manifest before, simultaneously or even after the disentanglement of their corresponding reservoirs.
Abstract In this paper, we calculate the concurrence for two entangled qubits that are immersed in either a homogeneous or a heterogeneous N-qubit environment. The concurrence for the discrete homogeneous environment was found to behave periodically depending on the interaction strengths ω S 1 S 2 and Γ. For the case of a heterogeneous environment, we set the interaction strength Γ Siεk as uniformly random. This case mimics of a noisy environment as it illustrates an asymptotic decay of entanglement. The sudden death behavior found in the heterogenous case becomes more prominent for larger N number of qubit environments, and no other entanglement is found as time t → ∞.
One of the main obstacles toward building efficient quantum computing systems is decoherence, where the inevitable interaction between the qubits and the surrounding environment leads to a vanishing entanglement. We consider a system of two interacting asymmetric two-level atoms (qubits) in the presence of pure and correlated dephasing environments. We study the dynamics of entanglement while varying the interaction strength between the two qubits, their relative frequencies, and their coupling strength to the environment starting from different initial states of practical interest. The impact of the asymmetry of the two qubits, reflected in their different frequencies and coupling strengths to the environment, varies significantly depending on the initial state of the system and its degree of anisotropy. For an initial disentangled, or a Werner, state, as the difference between the frequencies increases, the entanglement decay rate increases, with more persistence at the higher degrees of anisotropy in the former state. However, for an initial anti-correlated Bell state, the entanglement decays more rapidly in the symmetric case compared with the asymmetric one. The difference in the coupling strengths of the two qubits to the pure (uncorrelated) dephasing environment leads to higher entanglement decay in the different initial state cases, though the rate varies depending on the degree of anisotropy and the initial state. Interestingly, the correlated dephasing environment, within a certain range, was found to enhance the entanglement dynamics starting from certain initial states, such as the disentangled, anti-correlated Bell, and Werner, whereas it exhibits a decaying effect in other cases such as the initial correlated Bell state.