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arXiv:0910.5622 · Physical Review A

Mechanism of entanglement preservation

Qingjun Tong, Jun‐Hong An, Hong‐Gang Luo, C. H. Oh

Published May 24, 2010• 134 citations
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Abstract

We study the entanglement preservation of two qubits locally interacting with their reservoirs. We show that the existence of a bound state of the qubit and its reservoir and the non-Markovian effect are two essential ingredients and their interplay plays a crucial role in preserving the entanglement in the steady state. When the non-Markovian effect is neglected, the entanglement sudden death (ESD) is reproduced. On the other hand, when the non-Markovian is significantly strong but the bound state is absent, the phenomenon of the ESD and its revival is recovered. Our formulation presents a unified picture about the entanglement preservation and provides a clear clue on how to preserve the entanglement in quantum information processing.

DOI
10.1103/physreva.81.052330

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We study the entanglement preservation of two qubits locally interacting with their reservoirs. We show that the existence of a bound state of the qubit and its reservoir and the non-Markovian effect are two essential ingredients and their interplay plays a crucial role in preserving the entanglement in the steady state. When the non-Markovian effect is neglected, the entanglement sudden death (ESD) is reproduced. On the other hand, when the non-Markovian is significantly strong but the bound state is absent, the phenomenon of the ESD and its revival is recovered. Our formulation presents a unified picture about the entanglement preservation and provides a clear clue on how to preserve the entanglement in quantum information processing.
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.
Using the Shabani-Lidar post-Markovian master equation, we derive non-Markovian generalizations of important quantum decohering operations on single qubits. When environmental memory effects are being taken into account, both single-qubit coherence and two-qubit entanglement may be preserved over a longer period of time, in contrast to the corresponding situations where these are totally neglected. We argue that recognizing the fact that every environment is inherently non-Markovian could be the key to the resolution of the issue of entanglement sudden death.
We analyze the dynamics of the entanglement in two independent non-Markovian channels. In particular, we focus on the entanglement dynamics as a function of the initial states and the channel parameters like the temperature and the ratio rrr between ω0ω_0ω0​ the characteristic frequency of the quantum system of interest, and ωcω_cωc​ the cut-off frequency of Ohmic reservoir. We give a stationary analysis of the concurrence and find that the dynamic of non-markovian entanglement concurrence Cρ(t)\mathcal{C}_ρ(t)Cρ​(t) at temperature kBT=0k_BT=0kB​T=0 is different from the kBT>0k_BT>0kB​T>0 case. We find that "entanglement sudden death" (ESD) depends on the initial state when kBT=0k_BT=0kB​T=0, otherwise the concurrence always disappear at finite time when kBT>0k_BT>0kB​T>0, which means that ESD must happen. The main result of this paper is that the non-Markovian entanglement dynamic is fundamentally different from the Markovian one. In the Markovian channel, entanglement decays exponentially and vanishes only asymptotically, but in the non-Markovian channel the concurrence Cρ(t)\mathcal{C}_ρ(t)Cρ​(t) oscillates, especially in the high temperature case. Then an open-loop controller adjusted by the temperature is proposed to control the entanglement and prolong the ESD time.
Quantum entanglement manifests as a distinctive correlation between particles that transcends classical boundaries when their quantum states cannot be described independently. On the other hand, as quantum systems interact with their surroundings, decoherence emerges, leading to the gradual decay of quantum coherence and entanglement. In the case of entanglement, this is known as entanglement sudden death (ESD). Decoherence mechanisms are examined, focusing on how various environmental factors, such as thermal, electromagnetic, and collisional decoherence, influence the integrity of entangled states. The role of quantum noise, such as amplitude damping, phase damping, and depolarizing, is also analyzed. By integrating theoretical insights with experimental findings, this study highlights the delicate balance between maintaining entanglement and mitigating decoherence. The findings have significant implications for the development of quantum technologies, including quantum computing and quantum communication, where preserving entanglement is crucial for achieving robust and reliable performance.