Weak Measurements, Quantum State Collapse and the Born Rule
Apoorva Patel, Indian Institute of Science
Projective measurement is used as a fundamental axiom in quantum
mechanics, even though it is discontinuous and cannot predict which measured operator eigenstate will be observed in which experimental run. The probabilistic Born rule gives it an ensemble interpretation, predicting proportions of various outcomes over many experimental runs. Understanding gradual weak measurements requires replacing this scenario with a dynamical evolution equation for the collapse of the quantum state in individual experimental runs. That can help design optimal feedback for quantum control and error correction. We revisit the framework to model quantum measurement as a continuous nonlinear stochastic process. It combines attraction towards the measured operator eigenstates with white noise, and for a specific ratio of the two reproduces the Born rule. We emphasise some striking features of this result that can be experimentally tested. Furthermore, the stochastic noise is tied to the system-apparatus interaction and the amplification process in the detector.