Decomposing generalized measurements into continuous stochastic processes
Decomposing generalized measurements into continuous stochastic processes
复制标题
将广义测量分解为连续随机过程
DOI：
--
复制
发表时间：
2007
期刊：
影响因子：
--
通讯作者：
T. Brun
中科院分区：
文献类型：
--
作者：
M. Varbanov;T. Brun
量子理论中最广泛的测量概念之一是广义测量。另一种测量范式--自然产生于量子光学等领域--是连续时间测量的范式，可以被视为连续弱测量序列的极限。它们自然地被描述为随机过程，或依赖于时间的随机变量。我们证明了任何广义测量都可以分解为具有数学极限的弱测量序列，它是一个连续的随机过程。我们给出了任何广义测量的显式构造，并证明了所产生的连续演化在长时间限制下，以正确的概率将量子系统的状态崩塌到由广义测量分解所产生的终态之一。该结构的一个显著特征是存在反馈机制--在给定时间的瞬时选择弱测量取决于先前测量的结果。对于具有n个结果的广义测量，这一信息是由n维单形上的实n向量捕捉的，它服从简单的经典随机演化。
One of the broadest concepts of measurement in quantum theory is the generalized measurement. Another paradigm of measurement--arising naturally in quantum optics, among other fields--is that of continuous-time measurements, which can be seen as the limit of a consecutive sequence of weak measurements. They are naturally described in terms of stochastic processes, or time-dependent random variables. We show that any generalized measurement can be decomposed as a sequence of weak measurements with a mathematical limit as a continuous stochastic process. We give an explicit construction for any generalized measurement, and prove that the resulting continuous evolution, in the long-time limit, collapses the state of the quantum system to one of the final states generated by the generalized measurement, being decomposed, with the correct probabilities. A prominent feature of the construction is the presence of a feedback mechanism--the instantaneous choice weak measurement at a given time depends on the outcomes of earlier measurements. For a generalized measurement with n outcomes, this information is captured by a real n-vector on an n-simplex, which obeys a simple classical stochastic evolution.