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arXiv:1308.1665 · Physical Review A

Protecting quantum states from decoherence of finite temperature using weak measurement

Shuchao Wang, Zong‐Wen Yu, Wenjie Zou, Xiang‐Bin Wang

Published Feb 13, 2014• 124 citations
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Abstract

Exposed in the nonzero temperature environment, a quantum system can both lose and gain excitations by interacting with the environment. In this work, we show how to optimally protect quantum states and quantum entanglement in such a situation based on measurement reversal from weak measurement. In particular, we present explicit formulas of protection. We find that this scheme can circumvent the entanglement sudden death in certain conditions.

DOI
10.1103/physreva.89.022318

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Exposed in the nonzero temperature environment, a quantum system can both lose and gain excitations by interacting with the environment. In this work, we show how to optimally protect quantum states and quantum entanglement in such a situation based on measurement reversal from weak measurement. In particular, we present explicit formulas of protection. We find that this scheme can circumvent the entanglement sudden death in certain conditions.
Decoherence, often caused by unavoidable coupling with the environment, leads to degradation of quantum coherence. For a multipartite quantum system, decoherence leads to degradation of entanglement and, in certain cases, entanglement sudden death. Tackling decoherence, thus, is a critical issue faced in quantum information, as entanglement is a vital resource for many quantum information applications including quantum computing, quantum cryptography, quantum teleportation, and quantum metrology. Here, we propose and demonstrate a novel scheme to protect entanglement from decoherence. Our entanglement protection scheme makes use of the quantum measurement itself for actively battling against decoherence and it can effectively circumvent even entanglement sudden death (ESD).
Decoherence, which causes degradation of entanglement and in some cases entanglement sudden death, is a critical issue faced in quantum information. Protecting entanglement from decoherence, therefore, is essential in practical realization of quantum computing and quantum communication protocols. In this paper, we demonstrate a novel method to protect entanglement from amplitude damping decoherence via weak measurement and quantum measurement reversal. It is shown that even entanglement sudden death can be circumvented.
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.
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.
We demonstrate a method to preserve entanglement and improve fidelity of three-qubit quantum states undergoing amplitude-damping decoherence using weak measurement and quantum measurement reversal. It is shown that we are able to enhance entanglement to the greatest extent, and to circumvent entanglement sudden death by increasing the weak measurement strength both for the GHZ state and the W state. The weak measurement technique can also enhance the fidelity to the quantum region and even close to 1 for the whole range of the decoherence parameter in both of the two cases. In addition, the W state can maintain more fidelity than the GHZ state in the protection protocol. However, the GHZ state has a higher success probability than the W state.
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.