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Physical Review A

Protecting remote bipartite entanglement against amplitude damping by local unitary operations

Xiao-Lan Zong, Chao-Qun Du, Ming Yang, Qing Yang, Zhuo‐Liang Cao

Published Dec 30, 2014• 17 citations
Publisher

Abstract

Remote entanglement will inevitably decrease due to the interactions between quantum systems and their environments. Therefore protecting remote entanglement against decoherence is of great importance in realizing quantum communication and quantum comp utation. In this paper, we demonstrate that decoherence caused by weak-measurement-induced damping can be effectively suppressed by adding local unitary operation series on each qubit. The results show that the entanglement of the output state can approach that of the state before amplitude damping. The most distinct advantage of this entanglement protection scheme is that any unitary operation (except the identity operation) has this entanglement reversal effect on the amplitude-damped states. Furthermore, in each local unitary operation series, all the operations can be different from one other, and all the time intervals between any two adjacent operations can be different too. In addition, there is no need for the two remote users to synchronize their operations. Unlike most of the previous schemes, we do not assume the instantaneous local unitary operation, and each operation has a duration. All these advantages suggest that this remote entanglement protection scheme is much simpler and feasible than the previous ones, and we hope it can be implemented in the near future. Recently, Y. S. Kim et al. [Nat. Phys. 8, 117 (2012)] pointed out that ``pre-weak measurement $+$ amplitude damping $+$ bit-flipping operation $+$ post-weak measurement'' can actively combat specific decoherence. By combing our proposal with Kim et al.'s scheme, the protection performance can be greatly improved by replacing the bit-flipping operation with an arbitrary rotational operation around the $x$ axis, the number of the operations as well as the interval between any two adjacent operations all can be different, and the application range of the scheme can be greatly broadened.

DOI
10.1103/physreva.90.062345

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Remote entanglement will inevitably decrease due to the interactions between quantum systems and their environments. Therefore protecting remote entanglement against decoherence is of great importance in realizing quantum communication and quantum comp utation. In this paper, we demonstrate that decoherence caused by weak-measurement-induced damping can be effectively suppressed by adding local unitary operation series on each qubit. The results show that the entanglement of the output state can approach that of the state before amplitude damping. The most distinct advantage of this entanglement protection scheme is that any unitary operation (except the identity operation) has this entanglement reversal effect on the amplitude-damped states. Furthermore, in each local unitary operation series, all the operations can be different from one other, and all the time intervals between any two adjacent operations can be different too. In addition, there is no need for the two remote users to synchronize their operations. Unlike most of the previous schemes, we do not assume the instantaneous local unitary operation, and each operation has a duration. All these advantages suggest that this remote entanglement protection scheme is much simpler and feasible than the previous ones, and we hope it can be implemented in the near future. Recently, Y. S. Kim et al. [Nat. Phys. 8, 117 (2012)] pointed out that ``pre-weak measurement +++ amplitude damping +++ bit-flipping operation +++ post-weak measurement'' can actively combat specific decoherence. By combing our proposal with Kim et al.'s scheme, the protection performance can be greatly improved by replacing the bit-flipping operation with an arbitrary rotational operation around the xxx axis, the number of the operations as well as the interval between any two adjacent operations all can be different, and the application range of the scheme can be greatly broadened.
Entanglement is a vital resource for many quantum information processes. However, the unavoidable interaction between quantum system and its environment will lead to quantum decoherence. So protecting remote entanglement against decoherence is of great importance for realizing quantum information and quantum communication. In fact, there are many types of decoherences. Besides the depolarization and phase damping, amplitude damping is a typical decoherence mechanism. If we monitor the environments to guarantee that no excitation escapes from the system, the amplitude damping is modified into a weak measurement induced amplitude damping of the system. Amplitude damping decoherence can affect both single-qubit quantum states and multipartite entangled states. However, in most of previous quantum state protection schemes, the authors only pay attention to the single-qubit system or two-qubit system. Compared with bipartite entangled states, multipartite entangled states possess many advantages, but the entanglement property of multipartite entangled state is much more complicated than bipartite entanglement, so bipartite entanglement reversal (protection) scheme may not be suitable for multipartite case. Thus, in this paper, according to local pulse series and weak measurement, we propose an effective scheme for protecting two multipartite entangled states against amplitude damping, and these two multipartite states are Cluster state and Maximal slice (MS) state. Cluster state and MS state are two typical classes of multipartite entangled states, which play important roles in quantum computation and communication, respectively. These two states cannot be converted into each other with local operation and classical communication. Owing to its good operational and computable properties, here we choose negativity as a measure to quantify the multipartite entanglement. For the case of MS sate, no matter what the initial parameter is, when the local pulses are exerted on all qubits, the entanglement can be fixed around the entanglement of the initial state. Similarly, in the four-qubit cluster state case, if a series of flip operations is exerted on all qubits, it is shown that the multipartite entanglement can be recovered to the maximum 1.0. All these results show that this protocol can protect remote multipartite entanglement effectively. The physical mechanism behind this scheme is that the weak measurement combining with flip operation can balance the weight of different terms of the state, and move the entanglement toward the initial value. To summarize, our scheme is much simpler and feasible, which may warrant its experimental realization. Moreover, our scheme could be extended to protect other multipartite states.
High-dimensional quantum communication plays an important role in long-distance quantum communication. It is shown that two-qubit quantum entanglement can be protected from amplitude damping decoherence. We study the effect of amplitude damping decoherence on two-qubit high-dimensional quantum entanglement. The negativity for high-dimensional quantum entanglement with or without quantum weak measurement and the reversal in amplitude damping decoherence are presented. We found that nonmaximally entangled state may have better performance than maximally entangled state in amplitude damping decoherence. Moreover, we show that arbitrary high-dimensional quantum entanglement can be protected from amplitude damping decoherence by weak measurement and the reversal. The results of our protocol are in agreement with previous analysis for the case of qubits and qutrits.
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.
Quantum secure communication provides a new way for protecting the security of information. As an important component of quantum secure communication, remote state preparation (RSP) can securely transmit a quantum state from a sender to a remote receiver. The existence of quantum noise severely affects the security and reliability of quantum communication system. In this paper, we study the method for improving the efficiency of joint RSP (JRSP) subjected to noise with the help of weak measurement and its reversal measurement. Taking a GHZ based deterministic JRSP as an example, we utilize the technique of weak measurement and its reversal to suppress the effect of the amplitude-damping noise firstly. Our study shows that the fidelity of the output state can be improved in the amplitude-damping noise. We also study the effect of weak measurement and its reversal in other three types of noise usually encountered in real-world, namely, the bit-flip, phase-flip (phase-damping) and depolarizing noise. Our results show that the weak measurement has no effect for suppressing the bit-flip and phase-flip (phase-damping) noise, while has slight effect for suppressing the depolarizing noise. Our study is suitable for JRSP and RSP, and will be helpful for improving the efficiency of multiparticle entanglement based quantum secure communication in real implementation.
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.
Abstract Protection of entanglement of two qubits undergoing two independent amplitude damping channels using a local parity-time ( PT ) symmetric operation is exactly studied. First, the explicit expressions of concurrence quantifying the entanglement of two qubits with both local PT symmetric operation and two amplitude damping channels are obtained. Then, we give two schemes, i.e. prior and post PT symmetric operations, to show the performance of PT symmetric operation on entanglement dynamics of two qubits. By investigation, we find that the effect of prior PT symmetric operation schemes on the protection of entanglement of two qubits in the double channel case is superior to that of the single channel case. Conversely, the effect of post PT symmetric operation scheme on the protection of entanglement of two qubits in the single channel case is better than that in the double channel case. In other words, the local PT symmetric operation approach may have potential applications in combating amplitude damping decoherence.