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Weak measurements, quantum-state collapse, and the Born rule

Patel, Apoorva and Kumar, Parveen (2017) Weak measurements, quantum-state collapse, and the Born rule. In: PHYSICAL REVIEW A, 96 (2).

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Official URL: http://doi.org/10.1103/PhysRevA.96.022108

Abstract

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. We revisit the quantum trajectory framework that models quantum measurement as a continuous nonlinear stochastic process. We describe the ensemble of quantum trajectories as noise fluctuations on top of geodesics that attract the quantum state towards the measured operator eigenstates. In this effective theory framework for the ensemble of quantum trajectories, the measurement interaction can be specific to each system-apparatus pair, a context necessary for understanding weak measurements. Also in this framework, the constraint to reproduce projective measurement as per the Born rule in the appropriate limit requires that the magnitudes of the noise and the attraction are precisely related, in a manner reminiscent of the fluctuation-dissipation relation. This relation implies that both the noise and the attraction have a common origin in the underlying measurement interaction between the system and the apparatus. We analyze the quantum trajectory ensemble for the scenarios of quantum diffusion and binary quantum jump, and show that the ensemble distribution is completely determined in terms of a single evolution parameter. This trajectory ensemble distribution can be tested in weak measurement experiments. We also comment on how the required noise may arise in the measuring apparatus.

Item Type: Journal Article
Additional Information: Copy right for this article belongs to the AMER PHYSICAL SOC, ONE PHYSICS ELLIPSE, COLLEGE PK, MD 20740-3844 USA
Department/Centre: Division of Physical & Mathematical Sciences > Centre for High Energy Physics
Depositing User: Id for Latest eprints
Date Deposited: 01 Sep 2017 07:24
Last Modified: 01 Sep 2017 07:24
URI: http://eprints.iisc.ac.in/id/eprint/57703

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