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Optimal Measurements of Spin Direction

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Abstract

The accuracy of a measurement of the spin direction of a spin-s particle ischaracterized for arbitrary half-integral s. The disturbance caused by themeasurement is also characterized. The approach is based on that taken in severalprevious papers concerning joint measurements of position and momentum. Asin those papers, a distinction is made between the errors of retrodiction andprediction. Retrodictive and predictive error relationships are derived. The POVMdescribing the outcome of a maximally accurate measurement process isinvestigated. It is shown that if the measurement is retrodictively optimal, thenthe distribution of measured values is given by the initial state SU(2) Q-function.If the measurement is predictively optimal, then the distribution of measuredvalues is related to the final state SU(2) P-function. The general form of theunitary evolution operator producing an optimal measurement is characterized.

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  1. Department of Physics, Queen Mary and Westfield College, Mile End Rd, London, E1 4NS, United Kingdom

    D. M. Appleby

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  1. D. M. Appleby
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Appleby, D.M. Optimal Measurements of Spin Direction. International Journal of Theoretical Physics 39, 2231–2252 (2000). https://doi.org/10.1023/A:1003712030966

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