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Chinese Physics B

Optimizing quantum correlation dynamics by weak measurement in dissipative environment

Shao-Jiang Du, Yun‐Jie Xia, Deyang Duan, Lu Zhang, Qiang Gao

Published Mar 31, 2015• 1 citation
Publisher

Abstract

We investigate the protection of quantum correlations of two qubits in independent vacuum reservoirs by means of weak measurements. It is found that the weak measurement can reduce the amount of quantum correlation for one type of initial state at the beginning in a non-Markovian environment and meanwhile it can reduce the occurrence time of entanglement sudden death (ESD) in the process of time evolution. In a Markovian environment, the quantum entanglements of the two kinds of initial states decay rapidly and the weak measurement can further weaken the quantum entanglement, therefore in this case the entanglement cannot be optimized in the evolution process.

DOI
10.1088/1674-1056/24/4/044205

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We investigate the protection of quantum correlations of two qubits in independent vacuum reservoirs by means of weak measurements. It is found that the weak measurement can reduce the amount of quantum correlation for one type of initial state at the beginning in a non-Markovian environment and meanwhile it can reduce the occurrence time of entanglement sudden death (ESD) in the process of time evolution. In a Markovian environment, the quantum entanglements of the two kinds of initial states decay rapidly and the weak measurement can further weaken the quantum entanglement, therefore in this case the entanglement cannot be optimized in the evolution process.
The protection schemes of the entanglement in the system of two entangled atoms from nonMarkovian reservoirs via previous Weak measurement (pre-WM) and posterior Weak measurement reversal (post-WMR) are investigated. We firstly compare the effects of combination applying of pre-WM and post-WMR (scheme 1) and twice Weak measurements (WMs) (scheme 2) in the condition of different initial entangled states. The analysis indicates that the protection performance of scheme 1 is much better than that of scheme 2. The scheme 1 was utilized when the system of two entangled atoms suffers from the independent reservoirs. The numerical results show that the combination of pre-WM and post-WMR can effectively enhance entanglement and shorten the time of Entanglement sudden death (ESD) in non-Makovain environment. We have found the optimum of WM strengthens is drastically related to the initial entangled state.
Abstract The inevitable dissipative interaction of an entangled quantum system with its environment causes degradation in quantum correlations present in the system. This can lead to a finite-time disappearance of entanglement, which is known as Entanglement Sudden Death (ESD). Here, we consider an initially entangled qubit-qutrit system and a dissipative noise which leads to ESD, and propose a set of local unitary operations, which when applied on the qubit, qutrit, or both subsystems during the decoherence process, cause ESD to be hastened, delayed, or avoided altogether, depending on its time of application. Delay and avoidance of ESD may find practical application in quantum information processing protocols that would otherwise suffer due to short lifetime of entanglement. The physical implementation of these local unitaries is discussed in the context of an atomic system. The simulation results of such ESD manipulations are presented for two different classes of initially entangled qubit-qutrit systems. A prescription for generalization of this scheme to a qutrit-qutrit system is given. This technique for entanglement protection in the noisy environment is compared with other related techniques such as weak measurement reversal, dynamic decoupling, and quantum Zeno effect.
Abstract In this work, a scheme to protect quantum entanglement from a non‐Markovian noisy environment is proposed. By applying two quantum weak measurements before and after sending the quantum state into the noisy channel, the quantum state can be “pushed” closer to a decoherence‐free state, reducing decoherence during the time evolution. Then, the second weak measurement can partially retrieve the initial quantum state from the state corrupted by the noisy environment. The study involves a non‐Markovian dynamic equation to examine the impact of the memory effect on the protection scheme's performance. Various factors affecting the residual entanglement and the success probability are analyzed. The results suggest that two measurement strengths shall be chosen approximately in a linear relation, with the best ratio determined by the memory time of the environment. Additionally, it is demonstrated that the memory effect significantly enhances the protection efficiency. Lastly, the scheme's robustness against systematic errors is evaluated.
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.
In this research we analyze two models using the tensor network algorithm. The quantum correlations of a two-qubit system are first studied in different bosonic reservoirs. Both equilibrium and nonequilibrium scenarios are discussed. Non-Markovian effects can improve the survival time of the quantum correlations significantly and weaken the decoherence effect. Non-Markovian dynamics with existing memory can lead to entanglement rebirth in specific scenarios instead of the eventual entanglement decay or death seen in memoryless Markovian cases. The system reaches a steady state quickest in sub-Ohmic reservoirs and shows the most apparent non-Markovian behavior in super-Ohmic reservoirs. The Markovian approximation used in this paper is superior to that in the Bloch-Redfield master equation. The entanglement dynamics behaves similarly under different approaches when the system-bath coupling is weak and the memory effect is significant when the system-bath coupling is strong. We study not only the impact of the environment on quantum correlations, but also how to protect quantum correlations. Starting from a state in which the two ends are maximally entangled, a one-dimensional Aubry-Andr\'e chain model is also studied. We identify distinct phases by monitoring the imbalance dynamics. When the chain is closed, the imbalance dynamics behaves differently in various phases and so does the entanglement evolution between the chain's ends. When the first site couples to a bath, we find that the imbalance dynamics can still be an effective indicator to differentiate various phases in an early evolution stage since the imbalance dynamics is only remarkably affected at relatively high temperatures. The distribution of the eigenenergy of the system can account for it. The entanglement of the chain ends decays rapidly in all phases due to one of the ends being coupled to the bath directly. However, the entanglement of the chain ends will persist for a perceptible amount of time in the localization phase if the bath is coupled to the middle site of the chain. Our research shows that one can utilize the disordered environment as a buffer to protect quantum correlations.