On the Power of Weak Measurements in Separating Quantum States

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.

11 pages, 7 figures. To be published in Quantum Studies: Mathematics and Foundations

References in corpus (4)

• Complex weak values in quantum measurement
• Optimizing the Signal to Noise Ratio of a Beam Deflection Measurement with Interferometric Weak Values
• Optimal state discrimination with a fixed rate of inconclusive results: Analytical solutions and relation to state discrimination with a fixed error rate
• Null Values and Quantum State Discrimination