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Physical Review A

Witnessing the dynamics of entanglement and manipulating the sudden death of entanglement under the influence of a squeezed thermal reservoir

M. Hunza, Ming‐Da Huang, Qi Qin, Tasawar Abbas

Published Aug 29, 2025• 0 citations

Abstract

ThThis study investigates the entanglement dynamics of a bipartite system comprising two two-level atoms, initially prepared in a pure entangled state and independently coupled to spatially separated cavities under local squeezed thermal environments. We demonstrate that environmental interactions induce entanglement sudden death (ESD), leading to the abrupt loss of quantum correlations. To mitigate this effect, we propose a protocol involving local unitary operations—X gate ((1) ⊗(2)) and XX gate ((1) ⊗(2))—applied to the time-evolved state. We further analyze the impact of these operations under symmetric and asymmetric probability amplitudes of the atomic states, considering variations in thermal and squeezing parameters across different reservoirs. Our results show that these operations extend entanglement duration in specific reservoir conditions, while in the case of a vacuum reservoir, they transform ESD into asymptotic decay for both symmetric and asymmetric probability amplitudes of the atomic states. Moreover, independent variations of the thermal and squeezing parameters in each reservoir influence the dynamics of local gate operations, thereby affecting the overall entanglement evolution. Additionally, applying these operations at an earlier stage of the system's evolution can further delay ESD. This scheme offers valuable insights into entanglement behavior and its resilience under various noisy environmental conditions. ©2025 American Physical Society.

DOI: 10.1103/k9sg-c987

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We investigate the phenomenon of sudden death of entanglement in a high-dimensional bipartite system subjected to dissipative environments with an arbitrary initial pure entangled state between two fields in the cavities. We find that in a vacuum reservoir, the presence of the state where one or more than one (two) photons in each cavity are present is a necessary condition for the sudden death of entanglement. Otherwise entanglement remains for infinite time and decays asymptotically with the decay of individual qubits. For pure two-qubit entangled states in a thermal environment, we observe that sudden death of entanglement always occurs. The sudden death time of the entangled states is related to the number of photons in the cavities, the temperature of the reservoir and the initial preparation of the entangled states.

Entanglement plays a crucial role in quantum information protocols; thus the dynamical behavior of entangled states is of great importance. In this paper, we suggest a useful scheme that permits a direct measure of entanglement in a two-qubit cavity system. It is realized through cavity-QED technology utilizing atoms as flying qubits. To quantify entanglement we use the concurrence. We derive the conditions that ensure that the state remains entangled in spite of the interaction with the reservoir. The phenomenon of entanglement sudden death in a bipartite system subjected to a squeezed vacuum reservoir is examined. We show that the sudden death time of the entangled states depends on the initial preparation of the entangled state and the parameters of the squeezed vacuum reservoir.

We investigate the entanglement dynamics of two interacting qubits in a common vacuum environment. The inevitable environment interaction leads to entanglement sudden death (ESD) in a two qubit entangled state system. The entanglement dynamics can be modified by the use of local unitary operations (quantum gates), applied on the system during its evolution. We show that these operations not only delays or avoids the ESD but also advances the entanglement revival with high concurrence value depending on the time of operation. We have analytically found out different time windows for switching with different quantum gates so that the ESD can be completely avoided in the subsequent evolution of the system. Our result offers practical applications in the field of quantum information processing where the entanglement is a necessary resource.

By analytically solving the Lindblad form of the master equation, we investigate entanglement dynamics of two qubits coupled via the XY interaction, where each qubit is interacting with an independent reservoir with the squeezing parameters and squeezing angles. In the weak-squeezed reservoir, we show that the entanglement sudden death and entanglement sudden birth will happen for various entangled states. Some initial product states evolve into entangled ones, initially entangled states lose completely or partially their entanglement. The effects of varying the degree of entanglement of the initial states, the spin chain system parameters and different values of the degree of squeezing on the sudden death, revival and birth times are analyzed in detail. We also see that the steady state concurrence appears in the squeezed dissipative environments, which is affected by both the system parameters and the degree of squeezing.

We investigate the time evolution of entanglement of various entangled states of a two-qubit system exposed to either thermal or squeezed reservoirs. We show that, except for the vacuum reservoir, the sudden-death of entanglement always exists in the thermal and squeezed reservoirs. We present explicit expression for the sudden-death time of entanglement for various entangled states. We find that the sudden-death of entanglement results from the portion of the double excitation component in the initial entangled state. In this sense, the maximally entangled states of a two-qubit system that do not have the double excitation component is more robust against the quantum fluctuations of the vacuum reservoir.