On the Power of Weak Measurements in Separating Quantum States
arXiv:1501.02182 · doi:10.1007/s40509-015-0029-7
Abstract
We investigate the power of weak measurements in the framework of quantum state discrimination. First, we define and analyze the notion of weak consecutive measurements. Our main result is a convergence theorem whereby we demonstrate when and how a set of consecutive weak measurements converges to a strong measurement. Second, we show that for a small set of consecutive weak measurements, long before their convergence, one can separate close states without causing their collapse. We thus demonstrate a tradeoff between the success probability and the bias of the original vector towards collapse. Next we use post-selection within the Two-State-Vector Formalism and present the non-linear expansion of the expectation value of the measurement device's pointer to distinguish between two predetermined close vectors.
arXiv comment11 pages, 7 figures. To be published in Quantum Studies: Mathematics and Foundations
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