一维离散时间量子行走中依赖于方向的泡利噪声

中文摘要 AI 辅助

离散时间量子行走表现出对退相干高度敏感的弹道扩散。我们研究了在作用于硬币的泡利噪声下，一维离散时间量子行走的长时间动力学。选择幺正硬币使其不变布洛赫球轴与条件移位固定的轴正交，我们识别了与任一动力学轴对齐或与两者都正交的噪声的不同效应。利用傅里叶空间泡利超算符形式，我们推导了X、Y、Z和退极化噪声的前两个位置矩和长时间渐近行为的表达式。所有通道都诱导从弹道到扩散扩散的交叉，第二矩在长时间线性增长。接近该区域的方式依赖于通道：对于X、Z和退极化噪声是指数快速的，但对于Y噪声是代数的，具有主导的$t^{-1/2}$修正。位置分布保留不同的有限噪声特征，包括Y噪声的具有中心凹陷的高斯型轮廓。在最大噪声极限下，退极化、Y和Z噪声对任意初始硬币态产生经典二项分布，而X噪声仅在初始态沿噪声轴无分量时如此。因此，量子到经典的转变由噪声、相干行走动力学和初始态的相对对齐控制。

英文摘要

Discrete-time quantum walks exhibit ballistic spreading that is highly sensitive to decoherence. We study the long-time dynamics of a one-dimensional discrete-time quantum walk under Pauli noise acting on the coin. Choosing the unitary coin such that its invariant Bloch-sphere axis is orthogonal to the axis fixed by the conditional shift, we identify the distinct effects of noise aligned with either dynamical axis or orthogonal to both. Using a Fourier-space Pauli-superoperator formalism, we derive expressions for the first two position moments and long-time asymptotics for X-, Y-, Z-, and depolarizing noise. All channels induce a crossover from ballistic to diffusive spreading, with a second moment growing linearly at long times. The approach to this regime is channel dependent: it is exponentially fast for X-, Z-, and depolarizing noise, but algebraic, with a leading $t^{-1/2}$ correction, for Y-noise. The position distributions retain distinct finite-noise signatures, including a Gaussian-like profile with a central depression for Y-noise. In the maximal-noise limit, depolarizing, Y-, and Z-noise yield the classical binomial distribution for arbitrary initial coin states, whereas X-noise does so only when the initial state has no component along the noise axis. Thus, the quantum-to-classical transition is governed by the relative alignment of the noise, the coherent walk dynamics, and the initial state.

发表机构

• Departamento de Física, CUCEI, Universidad de Guadalajara（瓜达拉哈拉大学CUCEI物理系）
• Centro Universitario de Guadalajara, Universidad de Guadalajara（瓜达拉哈拉大学瓜达拉哈拉大学区）

机构由 AI 辅助整理，请以论文原文为准。