On the Power of Weak Measurements in Separating Quantum States

TL;DR

This paper explores how weak measurements can be used to distinguish quantum states without collapsing them, demonstrating convergence to strong measurements and a tradeoff between success probability and bias.

Contribution

It introduces a convergence theorem for weak measurements and shows their effectiveness in separating close quantum states before full collapse occurs.

Findings

Weak consecutive measurements can converge to strong measurements.

Weak measurements can distinguish close states without collapse.

There is a tradeoff between success probability and bias in weak measurements.

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.