Protecting the entanglement of two-qubit over quantum channels with memory via weak measurement and quantum measurement reversal

doi:10.1088/1674-1056/aba614

Abstract

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.

Keywords: quantum entanglement weak measurement and quantum measurement reversal quantum channel with memory concurrence

Received: 08 May 2020
Revised: 06 July 2020
Accepted manuscript online: 15 July 2020

Fund: the Natural Science Foundation of Shandong Province, China (Grant No. ZR2017MF040).

Corresponding Authors: ^†Corresponding author. E-mail: zhaojiaqiang@wfu.edu.cn

Cite this article:

Mei-Jiao Wang(王美姣), Yun-Jie Xia(夏云杰), Yang Yang(杨阳), Liao-Zhen Cao(曹连振), Qin-Wei Zhang(张钦伟), Ying-De Li(李英德), and Jia-Qiang Zhao(赵加强) Protecting the entanglement of two-qubit over quantum channels with memory via weak measurement and quantum measurement reversal 2020 Chin. Phys. B 29 110307

Fig. 1.

In the AD channel with memory, the concurrence $C_{d}^{A ψ (ϕ)}$ is the function of decoherent strength r and the memory parameter η for two initial entangled states | ψ 〉 = a|00〉 + d| 11 〉 and | ϕ 〉 = b| 01 〉 + c| 10 〉. We assume (a) | a | = 1 / 3, (b) | b | = 1 / 3.

Fig. 2.

In the AD channel with memory, χ^Aψ is a function of the weak measurement strength p and the memory parameter η for the initially entangled states | ψ 〉 = a| 00 〉 + d| 11 〉. We assume r = 0.2, (a) $a = \sqrt{0.1}$ ; (b) a = 1 / 3; (c) $a = \sqrt{0.2}$ ; (d) $a = \sqrt{0.4}$ ; (e) $a = \sqrt{2} / 2$ ; (f) $a = \sqrt{0.6}$ ; (g) $a = \sqrt{0.8}$ ; (h) $a = \sqrt{8} / 3$ ; (i) $a = \sqrt{0.9}$ .

Fig. 3.

In the AD channel with memory, the concurrence $C_{r}^{A ψ (ϕ)}$ is a function of WM strength p (q) for the two initially entangled states | ψ 〉 = a| 00 〉 + d| 11 〉 and | ϕ 〉 = b| 01 〉 + c| 10 〉. We assume r = 0.2, (a) | a | = 1 / 3, (b) | b | = 1/3.

Fig. 4.

In the quantum channels with memory, χ^A(B,D)ϕ is a function of the weak measurement strength p and the memory parameter η for the initially entangled state | ϕ 〉 = b| 01 〉 + c| 10 〉. We assume r = 0.2 and | b | = 1 / 3.

Fig. 5.

In the quantum channels with memory, the concurrence $C_{d}^{P (B, D) ψ (ϕ)}$ is a function of decoherent strength r and the memory parameter η for the two initial entangled states | ψ 〉 = a| 00 〉 + d| 11 〉 and | ϕ 〉 = b| 01 〉 + c| 10 〉. We assume | a | = 1 / 3 and | b | = 1 / 3. (a) PD channel; (b) BF channel; (c) depolarizing channel.

Fig. 6.

In the BF channel with memory, $χ^{B ψ}$ is a function of the weak measurement strength p and the memory parameter η for the initially entangled state | ψ 〉 = a| 00 〉 + d| 11 〉. We assume r = 0.2, (a) $a = \sqrt{0.1}$ ; (b) a = 1 / 3; (c) $a = \sqrt{0.2}$ ; (d) $a = \sqrt{0.4}$ ; (e) $a = \sqrt{2} / 2$ ; (f) $a = \sqrt{0.6}$ ; (g) $a = \sqrt{0.8}$ ; (h) $a = \sqrt{8} / 3$ ; (i) $a = \sqrt{0.9}$ .

Fig. 7.

In the BF channel with memory, the concurrence $C_{r}^{B ψ (ϕ)}$ is a function of weak measurement strength p (q) for two initially entangled states | ψ 〉 = a| 00 〉 + d| 11 〉 and | ϕ 〉 = b| 01 〉 + c| 10 〉. We assume r = 0.2, (a) | a | = 1 / 3, (b) | b | = 1 / 3.

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Protecting the entanglement of two-qubit over quantum channels with memory via weak measurement and quantum measurement reversal

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