量子控制和Strocchi映射
Quantum control and the Strocchi map
摘要：
通过用坐标和动量识别波函数的实部和虚部，量子演化可以被映射到经典的哈密顿系统上。除了辛形式，量子力学也有一个正定的实内积，它提供了测量过程的几何解释。它们一起赋予量子希尔伯特空间以凯勒流形的结构。量子控制是在这种情况下讨论。量子时间演化对应于光滑的哈密顿动力学，测量对应于相空间中的跳跃。这为量子控制增加了额外的力量，非幺正可控系统通过“测量加进化”变得可控。将量子演化描述为类经典相空间中的哈密顿动力学是将技术从经典控制转移到量子控制的适当设置。这说明了最优控制和滑模技术的讨论。
英文摘要：
Identifying the real and imaginary parts of wave functions with coordinates and momenta, quantum evolution may be mapped onto a classical Hamiltonian system. In addition to the symplectic form, quantum mechanics also has a positive-definite real inner product which provides a geometrical interpretation of the measurement process. Together they endow the quantum Hilbert space with the structure of a Käller manifold. Quantum control is discussed in this setting. Quantum time-evolution corresponds to smooth Hamiltonian dynamics and measurements to jumps in the phase space. This adds additional power to quantum control, non unitarily controllable systems becoming controllable by ``measurement plus evolution''. A picture of quantum evolution as Hamiltonian dynamics in a classical-like phase-space is the appropriate setting to carry over techniques from classical to quantum control. This is illustrated by a discussion of optimal control and sliding mode techniques.
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