In the paper, the Belavkin weighted square root measurement in infinite dimension is investigated. The question of uniqueness of such measurement is analyzed and some estimates for the probability of detection are obtained. Moreover, the asymptotics of the probability of detection and the probability of failure are derived in the situation when the pure states approach an orthonormal basis. The results in the paper generalize those obtained earlier for finite dimension.

中文翻译：

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加权量子测量

本文研究了无限维的 Belavkin 加权平方根测量。分析了这种测量的唯一性问题，并获得了对检测概率的一些估计。此外，检测概率和失效概率的渐近线是在纯态接近标准正交基的情况下推导出来的。论文中的结果概括了之前获得的有限维度的结果。