线性量子随机系统的纯级联综合
On synthesis of linear quantum stochastic systems by pure cascading
摘要：
最近，人们已经证明，一个任意的线性量子随机系统可以实现为一个级联连接的简单的一个自由度的量子谐振子与直接相互作用的哈密顿量，这是双线性的正则算子的振荡器。然而，从实验的角度来看，通过纯级联实现，没有直接相互作用的哈密顿量，将更容易实现，这就提出了一个自然的问题，即什么样的线性量子随机系统可以单独通过级联实现。本文给出了这类线性量子随机系统的精确刻画，并证明了在传递函数可实现的较弱意义下，所有无源线性量子随机系统都属于这类系统。给出了一个构造性的例子，说明了一个两自由度无源线性量子随机系统的传递函数的纯级联实现。
英文摘要：
Recently, it has been demonstrated that an arbitrary linear quantum stochastic system can be realized as a cascade connection of simpler one degree of freedom quantum harmonic oscillators together with a direct interaction Hamiltonian which is bilinear in the canonical operators of the oscillators. However, from an experimental point of view, realizations by pure cascading, without a direct interaction Hamiltonian, would be much simpler to implement and this raises the natural question of what class of linear quantum stochastic systems are realizable by cascading alone. This paper gives a precise characterization of this class of linear quantum stochastic systems and then it is proved that, in the weaker sense of transfer function realizability, all passive linear quantum stochastic systems belong to this class. A constructive example is given to show the transfer function realization of a two degrees of freedom passive linear quantum stochastic system by pure cascading.
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