Asymptotic evolution of random unitary operations
Asymptotic evolution of random unitary operations
复制标题
随机酉运算的渐近演化
DOI：
10.2478/s11534-010-0018-8
复制
发表时间：
2009
影响因子：
--
通讯作者：
I. Jex
中科院分区：
文献类型：
--
作者：
J. Novotny;G. Alber;I. Jex
我们分析了由随机酉运算的大量迭代引起的量子系统的渐近动力学。虽然一般来说，这些量子运算不能对角化，但证明了它们的渐近动力学是由一个可对角化的超算子描述的。我们证明了这种渐近动力学发生在一个典型的低维吸引子空间中，该空间与所应用的幺正运算的概率分布无关。这个向量空间是由与单位模的特征值相关的所有酉运算的特征向量张成的。迭代随机酉操作可能的渐近动力学的含义被提出，并举例说明了一个涉及随机控制非操作作用于两个量子位的例子。
We analyze the asymptotic dynamics of quantum systems resulting from large numbers of iterations of random unitary operations. Although, in general, these quantum operations cannot be diagonalized it is shown that their resulting asymptotic dynamics is described by a diagonalizable superoperator. We prove that this asymptotic dynamics takes place in a typically low dimensional attractor space which is independent of the probability distribution of the unitary operations applied. This vector space is spanned by all eigenvectors of the unitary operations involved which are associated with eigenvalues of unit modulus. Implications for possible asymptotic dynamics of iterated random unitary operations are presented and exemplified in an example involving random controlled-not operations acting on two qubits.
DOI：
10.1073/pnas.46.2.257
发表时间：
1960-02
影响因子：
11.1
作者：
J. Schwinger
通讯作者：
J. Schwinger