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Annalen der Physik

Entanglement Protection Using Weak Measurement in Non‐Markovian Environment

Xiu-Yi Yang, Feng Zhang, Hongjie Yin, Jing Nie

Published Jun 9, 2024• 2 citations
Publisher

Abstract

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.

DOI
10.1002/andp.202400091

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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.
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.
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.
Abstract The weak measurement (WM) and quantum measurement reversal (QMR) are crucial in protecting the collapse of quantum states. The idea of WM and QMR has recently been used to protect and enhance quantum correlations and universal quantum teleportation (UQT) protocols. Here, we study the quantum correlations, maximal fidelity, and fidelity deviation of the two-qubit negative quantum states developed using discrete Wigner functions with(without) WM and QMR. To take into account the effect of a noisy environment, we evolve the states via non-Markovian amplitude damping and random telegraph noise quantum channels. To benchmark the performance of negative quantum states, we calculate their success probability. We compare our results with the two-qubit maximally entangled Bell state. Interestingly, we observe that some negative quantum states perform better with WM and QMR than the Bell state for different cases under evolution via noisy quantum channels.
A protective scheme of quantum dense coding and quantum teleportation of the X-type initial state is proposed in amplitude damping noisy channel with memory using weak measurement and measurement reversal. Compared with the noisy channel without memory, the memory factor improves both the capacity of quantum dense coding and the fidelity of the quantum teleportation to a certain extent for the given damping coefficient. Although the memory factor can inhibit decoherence in some degree, it cannot eliminate it completely. In order to further overcome the influence of the damping coefficient, the weak measurement protective scheme is proposed, which found that the capacity and the fidelity can be efficiently improved by adjusting weak measurement parameter. Another practical conclusion is that, among the three initial states, the weak measurement protective scheme has the best protective effect on the Bell-state in terms of the capacity and the fidelity. For the channel with no memory and full memory, the channel capacity of quantum dense coding reaches two and the fidelity of quantum teleportation reaches one for the bit system; the Bell system can recover the initial state completely with a certain probability. It can be seen that the entanglement of the system can be well protected by the weak measurement scheme, which provides a good support for the realization of quantum communication.
In this paper, we investigate the entanglement dynamics of a two-qubit entangled state coupled with its noisy environment, and plan to utilize weak measurement and quantum reversal measurement to study the entanglement dynamics under different decoherence channels in noninertial frames. Through the calculations and analyses, it is shown that the weak measurement can prevent entanglement from coupling to the amplitude damping channel, while the system is under the phase damping and flip channels. This protection protocol cannot prevent entanglement but will accelerate the death of entanglement. In addition, if the system is in the noninertial reference frame, then the effect of weak measurement will be weakened for the amplitude damping channel. Nevertheless, for other decoherence channels, the Unruh effect does not affect the quantum weak measurement, the only exception is that the maximum value of entanglement is reduced to √2/2 of the original value in the inertial frames.
Addressing various types of decoherence is of paramount importance for employing entanglement in quantum information processing and quantum computing. In this paper, we propose two schemes to manipulate entanglement of two qubits stored in a common environment by means of combined weak measurements and quantum measurement reversals. We derive the explicit conditions for the measurement strengths under which at any time and for any initial states the qubits' entanglement can be protected quite well with a reasonable finite success probability. Moreover, the two schemes enable us in principle to achieve the maximal entanglement or to restore the initial state (entanglement) of the qubits.