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Physical Review A

Manipulating entanglement of two qubits in a common environment by means of weak measurements and quantum measurement reversals

Zhong‐Xiao Man, Yun‐Jie Xia, Nguyen Ba An

Published Jul 23, 2012• 106 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.86.012325

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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.
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 consider two entangled qubits, each of which is coupled to its own reservoir, so that their entanglement degrades with time. To enhance the qubits' entanglement at a time during the evolution we propose a proper combination of pre- and postmeasurements to be performed locally on individual qubits. The premeasurements are weak measurements, but the postmeasurements may be either quantum measurement reversals or weak measurements again, depending on the situation at the time they are applied. Given the parameters of the initial qubits' state, the premeasurements' strength, and the evolution time, we establish the optimal conditions for the postmeasurements so that the qubits' entanglement becomes the largest possible. Actually, by our scheme, less entangled qubits can evolve into more entangled ones with a finite probability, or even into a near-maximally entangled state but with a vanishingly low probability. We also examine the entanglement distribution among different pairs of subsystems involved and find out that the pairwise concurrence dynamics in our scheme differs strikingly from that in the situation without any control actions.
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.
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.
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.