Sequential generalized measurements: Asymptotics, typicality, and emergent projective measurements
Wen-Long Ma, Shu‐Shen Li, Ren‐Bao Liu
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, when the measurement operators are normal and commuting with each other. Specifically, a selective projective measurement arises from a set of typical sequences of selective generalized measurements. We also 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, which can have applications in readout, initialization, and feedback control of a quantum system. As an example, we present a protocol to measure the modular excitation numbers of a bosonic mode with an ancilla qubit.