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Laser Physics

Protecting high-dimensional quantum entanglement from the amplitude-phase decoherence sources by weak measurement and reversal

Wenjuan Li, Yun-Hui Zhao, Yang Leng

Published May 3, 2019• 11 citations
Publisher

Abstract

Abstract Entangled states with high-dimensional systems have been investigated widely because of its various advantages. This paper investigates the effect of the weak measurement and reversal (WMR) on the protection of the entanglement for an arbitrarily entangled qutrit–qutrit state from the amplitude-phase decoherence sources. By solving the master equation of the qutrit–qutrit system, we numerically get the maximal amount of entanglement. The numerical results show explicitly that the WMR operation indeed helps for protecting entanglement from amplitude-phase decoherence. In particular, WMR can protect entanglement more efficiently in the case of strong decay rates than those with small decay rates. These results shed new light on the protection of high-dimensional quantum entanglement in a complex quantum environment.

DOI
10.1088/1555-6611/ab126e

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Abstract Entangled states with high-dimensional systems have been investigated widely because of its various advantages. This paper investigates the effect of the weak measurement and reversal (WMR) on the protection of the entanglement for an arbitrarily entangled qutrit–qutrit state from the amplitude-phase decoherence sources. By solving the master equation of the qutrit–qutrit system, we numerically get the maximal amount of entanglement. The numerical results show explicitly that the WMR operation indeed helps for protecting entanglement from amplitude-phase decoherence. In particular, WMR can protect entanglement more efficiently in the case of strong decay rates than those with small decay rates. These results shed new light on the protection of high-dimensional quantum entanglement in a complex quantum environment.
Abstract Based on the quantum technique of environment-assisted measurement and reversal (EMR), we propose a scheme to restore the qutrit–qutrit entanglement from amplitude-phase damping decoherence. By solving the master equation, we get the exact analytical or numerical simulation expressions of the optimal final restoration, showing explicitly that the EMR does indeed restore the qutrit-qutrit entanglement to the original value. This sheds new light on the protection of high-dimensional quantum entanglement in a complex quantum environment.
Protection of entanglement from disturbance of the environment is an essential task in quantum information processing. We examine the validity and limitation of the weak measurement and reversal (WMR) operation in the protection of distributed entanglement from various decoherence sources. Since the entanglement variation can be investigated analytically for an arbitrarily entangled bipartite pure state under three kinds of typical noisy quantum channels, we show explicitly that the WMR operation indeed helps for protecting distributed entanglement from amplitude damping and phase damping, but not for depolarizing. Experimental feasibility for testing our results is discussed using current laboratory techniques.
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.
Abstract Based on the quantum technique of environment-assisted measurement and reversal (EMR), we propose a scheme to restore the entanglement from amplitude damping decoherence. In particular, we examine two typical families of initially entangled qubit–qutrit states and derive the exact analytical expressions of the optimal final restoration, showing explicitly that the EMR does indeed can recovery qubit–qutrit entanglement. This sheds new light on the protection of high-dimensional quantum entanglement in complex quantum environment.
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.