弱测量对四个量子比特量子态的保护

The protection of qudit states by weak measurement

廖湘萍等(Chin.Phys.B 23 020304,2014)指出弱测量和弱测量反转操作可以保护三个量子比特的纠缠,提高保真度.本文将弱测量方法推广至四个量子比特的情况,研究了几种典型四个量子比特量子态的演化.结果表明:在振幅阻尼通道中,弱测量方法能够有效地提高系统量子态的保真度.分析了影响量子态保真度的各种因素,对比了不同量子态的演化特征,划分了量子态保真度提高的敏感区域.最后,对弱测量方法抑制量子态衰减的内在机制做了合理的物理解释.

Liao Xiang-Ping et al. （Chin. Phys. B 23 020304, 2014） pointed out that the method of weak measurement and quantum weak measurement reversal can protect entanglement and improve the fidelity of three-qubit quantum state. We generalize the method of weak measurement to the case of qudit state in this paper. By using the operation of weak measurement and quantum weak measurement reversal, we investigate the evolution dynamics of fidelity and fidelity improvement for qudit state under amplitude damping decoherence. We compare two kinds of operations： one is to let the input qudit state cross the amplitude damping decoherence directly, and the other one is that we first make a weak measurement operation on the input qudit state, then through the amplitude damping decoherence, finally an operation of quantum weak measurement reversal is done with the output qudit state. We discuss the GHZ state, W state, CL state and some special separable states exactly and obtain the analytic expressions of fidelity and fidelity improvement for qudit state before and after the weak measurement and quantum weak measurement reversal operation. According to the analytic expressions we plot the evolution curves against its corresponding parameters. The effects of corresponding parameters are discussed and a susceptible protection region of the qudit state is also given in the context. The results show that the structure of qudit state is the determined factor to the effect of weak measurement and quantum weak measurement reversal. There are some different effects on the different structured qudit states. For entangled state, the fidelity of qudit GHZ state can be protected in a relatively big evolution region, most part of the fidelity improvement is in the upper part of the zero reference plane. While the fidelity of qudit W state can be improved effectively in the whole evolution region, which is a perfect protection. The evolution regulations of qudit CL state and Dick state are between evolution regulations of the GHZ state and W state. When we input some special separable qudit states which have similar structures to W state, their fidelity and fidelity improvement are almost the same as W state＇s. It is demonstrated that the structure of qudit state is important for the weak measurement in a step. This work is meaningful for the quantum information process.