According to the map of a qubit, a scheme for protecting entanglement of two-qubit by the weak measurements at finite temperature is proposed. Since the choices of the channel parameters and initial states are very different for different weak measurement strengths, two local unitary equivalent initial entangled states |ψ> and |φ> are chosen. Weak measurements are performed when two initial entangled states go through the generalized amplitude damping channel, and the analytical expressions of getting maximum concurrence entanglement Cr and weak measurement parameters m and n can be obtained by performing an overall optimization for four weak measurement parameters. What is more, the relationship between the weak measurement parameters and the channel parameters is further explored. Theoretical results show the entanglement protection project based on weak measurements can effectively enhance the entanglement and even prevent the sudden death of entanglement in some cases. When the channel parameter r is fixed, for different values of parameter p, the concurrence is centered at p = 0.5, and the weak measurement parameters of the maximum concurrence entanglement are the same as those for initial state |ψ>, while they are different for initial state |φ>. Under the condition of different values of r, for the fixed p and initial state |ψ> or |φ>, the weak measurement parameters remain constant as the entanglement reaches the maximum and the concurrence decreases with the increase of parameter r. Through the analysis of channel parameters, higher entanglement can be obtained by choosing appropriate channel parameters and initial state.
According to the map of a qubit, a scheme for protecting entanglement of two-qubit by the weak measurements at finite temperature is proposed. Since the choices of the channel parameters and initial states are very different for different weak measurement strengths, two local unitary equivalent initial entangled states |ψ> and |φ> are chosen. Weak measurements are performed when two initial entangled states go through the generalized amplitude damping channel, and the analytical expressions of getting maximum concurrence entanglement Cr and weak measurement parameters m and n can be obtained by performing an overall optimization for four weak measurement parameters. What is more, the relationship between the weak measurement parameters and the channel parameters is further explored. Theoretical results show the entanglement protection project based on weak measurements can effectively enhance the entanglement and even prevent the sudden death of entanglement in some cases. When the channel parameter r is fixed, for different values of parameter p, the concurrence is centered at p = 0.5, and the weak measurement parameters of the maximum concurrence entanglement are the same as those for initial state |ψ>, while they are different for initial state |φ>. Under the condition of different values of r, for the fixed p and initial state |ψ> or |φ>, the weak measurement parameters remain constant as the entanglement reaches the maximum and the concurrence decreases with the increase of parameter r. Through the analysis of channel parameters, higher entanglement can be obtained by choosing appropriate channel parameters and initial 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.
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.
We investigate the entanglement protection of a hybrid qubit–qutrit system under amplitude damping decoherence by employing weak measurement and reversal. We examine two typical families of initially entangled qubit–qutrit states (i.e. one-parameter and two-parameter qubit–qutrit states). We find that the qubit–qutrit entanglement decays monotonically as the decoherence strength increases, and may go through a sudden death for some initial states. However, we can completely defeat amplitude damping decoherence and recover the initial entanglement perfectly for any initial states by means of the combination of prior weak measurement and subsequent optimal weak measurement reversal. The only price that we have to pay is the very low success probability.
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.
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.
In practical applications, quantum systems work in a finite-temperature environment. Quantum entanglement is inevitably destroyed by the thermal noise. Here we experimentally demonstrate the protection of entanglement on the platform of linear optics. The finite-temperature thermal noise is described by the generalized amplitude-damping channel. By performing optimal pre- and postchannel weak measurements, we successfully protect the entanglement from the generalized amplitude-damping channel. Compared with the unprotected case, the quantum coherence is recovered, and the entanglement is enhanced. The demonstrated protocol may have further applications in superconducting quantum qubits.