AI 中文总结
该研究为群协变量子测量构建框架，从彼得 - 外尔分解出发构造协变测量算符，针对SU(2)得出封闭形式的跃迁核等，建立相关特性及描述，其解析预测与数值模拟相符，为表示空间上的协变量子测量提供随机描述。
AI 中文摘要
我们开发了一个用于群协变量子测量的框架，其中不可约表示扇区之间的测量诱导跃迁由表示空间上的随机过程描述。从彼得 - 外尔分解开始，我们从不可约张量算符构造协变测量算符，并表明对于对称不变态，测量通道简化为表示图上的马尔可夫过程。我们进一步表明测量算符的解析性通过杉浦定理约束探测器谱，从而激发了一类指数衰减探测器模型。专门针对SU(2)，我们以封闭形式获得跃迁核，建立可逆性和相关的不变测度，并推导诱导动力学的连续福克 - 普朗克描述。发现漂移和扩散系数的解析预测与数值模拟一致。我们的结果为表示空间上重复的协变量子测量提供了随机描述。
英文摘要
We develop a framework for group-covariant quantum measurements in which measurement-induced transitions between irreducible representation sectors are described by a stochastic process on representation space. Starting from the Peter-Weyl decomposition, we construct covariant measurement operators from irreducible tensor operators and show that, for symmetry-invariant states, the measurement channel reduces to a Markov process on the representation graph. We further show that analyticity of the measurement operator constrains the detector spectrum through Sugiura's theorem, motivating a class of exponentially decaying detector models. Specializing to SU(2), we obtain the transition kernel in closed form, establish reversibility and the associated invariant measure, and derive a continuum Fokker-Planck description of the induced dynamics. Analytical predictions for the drift and diffusion coefficients are found to agree with numerical simulations. Our results provide a stochastic description of repeated covariant quantum measurements on representation space.
Comments17 pages, 5 figures
