论文标题
Pontryagin的最大原理在耗散系统中的量子计量学
Application of Pontryagin's Maximum Principle to Quantum Metrology in Dissipative Systems
论文作者
论文摘要
最佳控制理论，也称为蓬蒂拉金的最大原理，在存在分解的情况下应用于量子参数估计。设计了一个有效的程序来计算有关控制参数的量子渔民信息的梯度，并用于构建最佳控制协议。提出的程序将控制问题保持在时间不变的形式中，以便适用于Pontryagin的最大原理的一阶和二阶最佳条件；当最佳控制包含奇异的弧线时，二阶条件被证明至关重要。具体而言，我们寻找最大化量子Fisher信息的最佳控制，以解决“扭曲和转弯”问题。我们发现，最佳控制是奇异的，而没有耗散，但是一旦引入了量子反应，可能会变得无限。需要一个振幅约束来保证有界解决方案。凭借量子的解相关，最大的量子渔民信息在有限的时间内发生在有限的时间，而渐近值取决于特定的退积通道和对价的控制。
Optimal control theory, also known as Pontryagin's Maximum Principle, is applied to the quantum parameter estimation in the presence of decoherence. An efficient procedure is devised to compute the gradient of quantum Fisher information with respect to the control parameters and is used to construct the optimal control protocol. The proposed procedure keeps the control problem in the time-invariant form so that both first-order and second-order optimality conditions derived from Pontryagin's Maximum Principle apply; the second-order condition turns out to be crucial when the optimal control contains singular arcs. Concretely we look for the optimal control that maximizes quantum Fisher information for "twist and turn" problem. We find that the optimal control is singular without dissipation but can become unbounded once the quantum decoherence is introduced. An amplitude constraint is needed to guarantee a bounded solution. With quantum decoherence, the maximum quantum Fisher information happens at a finite time due to the decoherence, and the asymptotic value depends on the specific decoherence channel and the control of consideration.
