连续时间抽象量子游荡的量子参数估计

Quantum Parameter Estimation ofContinuous Time AbstractQuantum Walk

摘要: 量子游荡作为经典随机游荡的量子类似物，广泛应用于量子信息理论。 在量子参数估计中，量子 系统对参数进行测量和估计，在理论和实际中都有重要的意义。 本文考虑一类作用于平方可积 Bernoulli 躁声泛函空间上的连续时间抽象量子游荡，给出了该量子游荡的演化方程。 针对该类 量子游荡讨论相应量子态估计问题，提出具体参数估计方案，证明了该估计方案的无偏性和相合性。

Abstract: As a quantum analogue of classical random walk, quantum walk is widely used in quantum information theory. In quantum parameter estimation, the measuremen- t and estimation of parameters by quantum systems is of great significance in both theory and practice. In this paper, we consider a class of continuous-time abstract quantum walk acting on square integrable Bernoulli noise functional space. The evolu- tion equation of the quantum walk is given. In view of this kind of quantum walk, the corresponding quantum state estimation problem is discussed, a specific parameter estimation scheme is proposed, and the unbiased and compatible estimation scheme of the estimation scheme is proved.