Abstract
We discuss quantum mechanical detection models in the weak limit in the context of conservation laws of physical quantities. In particular, we analyze what kind of system–detector interaction can preserve the global conservation or the related symmetry, and how the final measurement on the detector affects the measured observable of the systems and its presumed conservation. It turns out that the order of noncommuting measurements results in observable differences on the level of third-order correlations functions.
Highlights
Conservation laws are important in both classical and quantum mechanics
A similar construction is in general not possible for conserved but not superconserved quantities such as energy, momentum, and angular momentum, whose conservation is apparently violated in weak measurements even if an appropriate symmetry results in a classical conservation law
We propose an experiment to demonstrate the failure of a conservation principle for angular momentum in third order correlations in weak measurements
Summary
Conservation laws are important in both classical and quantum mechanics. The classical Noether theorem [1] links the conservation of certain quantities to the invariance of the dynamics of a system under specific transformations. The noise is unavoidable if the measurement is so weak that it does not disturb the measured system but can be clearly identified and removed by a deconvolution or subtracted from correlations to get the underlying quantum statistics This subtraction would occur in classical noisy measurements and cannot alone dismiss the objective reality reconstructed from such measurements. We define superconservation in terms of the restricted set of measurable observables that commute with a particular observable and will construct general measurements compatible with superconservation Such measurements can change the superconserved quantity, e.g. the charge, but only in an incoherent way. A similar construction is in general not possible for conserved but not superconserved quantities such as energy, momentum, and angular momentum, whose conservation is apparently violated in weak measurements even if an appropriate symmetry results in a classical conservation law. The violation of conservation appears in third-order time correlations as
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