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Laser Physics

Improving tripartite entanglement in open system by weak measurement and quantum measurement reversal

Yunhai Zhang, Yun‐Jie Xia

Published Apr 8, 2015• 4 citations
Publisher

Abstract

Qubits A, B and C, initially prepared in a like-GHZ state, are distributed to three remote receivers through a decoherence environment. A weak measurement is firstly performed on each qubit before experiencing the decoherence channel, and then the receivers carry out a quantum measurement reversal on individual qubit after receiving them. The qubits’ entanglement is evaluated by means of negativity. The results show the pre- and post-measurements’ strength has an important influence on tripartite entanglement for the initially given state, and proper pre- and post-measurements’ strength always effectively improves tripartite entanglement, which is significant to protect entanglement from decoherence.

DOI
10.1088/1054-660x/25/5/055201

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Qubits A, B and C, initially prepared in a like-GHZ state, are distributed to three remote receivers through a decoherence environment. A weak measurement is firstly performed on each qubit before experiencing the decoherence channel, and then the receivers carry out a quantum measurement reversal on individual qubit after receiving them. The qubits’ entanglement is evaluated by means of negativity. The results show the pre- and post-measurements’ strength has an important influence on tripartite entanglement for the initially given state, and proper pre- and post-measurements’ strength always effectively improves tripartite entanglement, which is significant to protect entanglement from decoherence.
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.
In practical application, since quantum entanglement is inevitably destroyed by thermal noise resulted from environment, protecting entanglement from decoherence in thermal bath environment becomes a critically important issue in the field of quantum information. In this work, we propose a scheme to protect the tripartite Greenberger–Horne–Zeilinger (GHZ) entanglement state subjected to the generalized amplitude damping (GAD) channel based on the quantum technique of weak measurement (WM) and quantum measurement reversal (QMR). By optimizing the strengths of WM and QMR, the decoherence caused by the channel can be effectively suppressed. The results show that after performing the optimal pre- and post-channel weak measurement, the negativity of the GHZ state can be effectively improved with a certain probability, and the phenomenon of sudden death can be delayed to a certain degree. This scheme can be applied to the decoherence suppression of GAD channel at finite temperature.
Liao Xiang-Ping et al.(Chin. Phys. B 23 020304, 2014) pointed out that the method of weak measurement and quantum weak measurement reversal can protect entanglement and improve the fidelity of three-qubit quantum state. We generalize the method of weak measurement to the case of qudit state in this paper. By using the operation of weak measurement and quantum weak measurement reversal, we investigate the evolution dynamics of fidelity and fidelity improvement for qudit state under amplitude damping decoherence. We compare two kinds of operations: one is to let the input qudit state cross the amplitude damping decoherence directly, and the other one is that we first make a weak measurement operation on the input qudit state, then through the amplitude damping decoherence, finally an operation of quantum weak measurement reversal is done with the output qudit state. We discuss the GHZ state, W state, CL state and some special separable states exactly and obtain the analytic expressions of fidelity and fidelity improvement for qudit state before and after the weak measurement and quantum weak measurement reversal operation. According to the analytic expressions we plot the evolution curves against its corresponding parameters. The effects of corresponding parameters are discussed and a susceptible protection region of the qudit state is also given in the context. The results show that the structure of qudit state is the determined factor to the effect of weak measurement and quantum weak measurement reversal. There are some different effects on the different structured qudit states. For entangled state, the fidelity of qudit GHZ state can be protected in a relatively big evolution region, most part of the fidelity improvement is in the upper part of the zero reference plane. While the fidelity of qudit W state can be improved effectively in the whole evolution region, which is a perfect protection. The evolution regulations of qudit CL state and Dick state are between evolution regulations of the GHZ state and W state. When we input some special separable qudit states which have similar structures to W state, their fidelity and fidelity improvement are almost the same as W state’s. It is demonstrated that the structure of qudit state is important for the weak measurement in a step. This work is meaningful for the quantum information process.
We demonstrate a method to preserve entanglement and improve fidelity of three-qubit quantum states undergoing amplitude-damping decoherence using weak measurement and quantum measurement reversal. It is shown that we are able to enhance entanglement to the greatest extent, and to circumvent entanglement sudden death by increasing the weak measurement strength both for the GHZ state and the W state. The weak measurement technique can also enhance the fidelity to the quantum region and even close to 1 for the whole range of the decoherence parameter in both of the two cases. In addition, the W state can maintain more fidelity than the GHZ state in the protection protocol. However, the GHZ state has a higher success probability than the W state.
Based on the quantum technique of the weak measurement and quantum measurement reversal (WMR), we propose a scheme to protect entanglement for an entangled two-qubit pure state from four typical quantum noise channels with memory, i.e., the amplitude damping channel, the phase damping channel, the bit flip channel, and the depolarizing channel. For a given initial state | ψ 〉 = a| 00 〉 + d| 11 〉, it is found that the WMR operation indeed helps to protect entanglement from the above four quantum channels with memory, and the protection effect of WMR scheme is better when the coefficient a is small. For the other initial state | ϕ 〉 = b| 01 〉 + c| 10 〉, the effect of the protection scheme is the same regardless of the coefficient b and the WMR operation can protect entanglement in the amplitude damping channel with memory. Moreover, the protection of entanglement in quantum noise channels without memory in contrast to the results of the channels with memory is more effective. For | ψ 〉 or | ϕ 〉, we also find that the memory parameters play a significant role in the suppression of entanglement sudden death and the initial entanglement can be drastically amplified. Another more important result is that the relationship between the concurrence, the memory parameter, the weak measurement strength, and quantum measurement reversal strength is found through calculation and discussion. It provides a strong basis for the system to maintain maximum entanglement in the nosie channel.
Entanglement protection from noisy environments is an essential task in practical quantum information and communication. In this paper, we investigate the entanglement recovery of an amplitude-damped tripartite GHZ state by a weak-measurement reversal procedure. In particular, we emphasize the key importance of the inequivalency of probability amplitudes of the tripartite system under the recovery technique. We explore the maximal and non-maximal tripartite entangled state scenarios under amplitude damping noise in the absence and presence of weak measurement reversal procedures. Importantly, the non-maximal entangled state turns out to be a good choice for the entanglement recovery via weak-measurement reversal procedure.