Sequential generalized measurements: Asymptotics, typicality and emergent projective measurements

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.

8 pages, 2 figures (+6 pages supplement)

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Cited by in corpus (5)

• Theory of Metastability in Discrete-Time Open Quantum Dynamics
• How coherence measurements of a qubit steer its quantum environment
• Channel-based framework for phase esimation of multiple eigenvalues
• Efficient nonclassical state preparation via generalized parity measurement
• General Approach to Error Detection of Bosonic Codes via Phase Estimation