Sequential generalized measurements: Asymptotics, typicality and emergent projective measurements

TL;DR

This paper proves that projective measurements can be constructed from sequential generalized measurements in the asymptotic limit, providing an explicit scheme using a single ancilla qubit, which advances understanding in quantum measurement theory.

Contribution

It offers a rigorous proof that projective measurements emerge from sequential generalized measurements and presents a practical scheme for their construction.

Findings

Projective measurements arise from typical sequences of generalized measurements asymptotically.

A single ancilla qubit suffices to implement the construction.

The scheme applies to generic quantum systems.

Abstract

The relation between projective measurements and generalized quantum measurements is a fundamental problem in quantum physics, and clarifying this issue is also important to quantum technologies. While it has been intuitively known that projective measurements can be constructed from sequential generalized or weak measurements, there is still lack of a proof of this hypothesis in general cases. Here we prove it from the perspective of quantum channels. We show that projective measurements naturally arise from sequential generalized measurements in the asymptotic limit. Specifically, a selective projective measurement arises from a set of typical sequences of selective generalized measurements. We provide an explicit scheme to construct projective measurements of a quantum system with sequential generalized measurements. Remarkably, a single ancilla qubit is sufficient to mediate sequential generalized measurements for constructing arbitrary projective measurements of a generic system.