Constrained reachability is a kind of quantitative path property, which is generally specified by multiphase until formulas originated in continuous stochastic logic. In this paper, through proposing a positive operator valued measure on the set of infinite paths, we develop an exact method to solve the constrained reachability problem for quantum Markov chains. The convergence rate of the reachability is also obtained. We then analyse the complexity of the proposed method, which turns out to be in polynomial-time w.r.t. the size of the classical state space and the dimension of the accompanied Hilbert space. Finally, our method is implemented and applied to a simple quantum protocol.

中文翻译：

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测量量子马尔可夫链中的受限可达性

约束可达性是一种量化的路径性质，一般用多相直到公式来指定，直到公式起源于连续随机逻辑。在本文中，通过在无限路径集上提出一个正算子值度量，我们开发了一种精确的方法来解决量子马尔可夫链的约束可达性问题。也得到了可达性的收敛速度。然后我们分析了所提出方法的复杂性，结果证明它是多项式时间的，与经典状态空间的大小和伴随的希尔伯特空间的维数有关。最后，我们的方法被实现并应用于一个简单的量子协议。