Directly measuring mean and variance of infinite-spectrum observables such as the photon orbital angular momentum

Bruno Piccirillo (), Sergei Slussarenko, Lorenzo Marrucci () and Enrico Santamato
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Bruno Piccirillo: Università di Napoli Federico II, Compl. University di Monte S. Angelo
Sergei Slussarenko: Università di Napoli Federico II, Compl. University di Monte S. Angelo
Lorenzo Marrucci: Università di Napoli Federico II, Compl. University di Monte S. Angelo
Enrico Santamato: Università di Napoli Federico II, Compl. University di Monte S. Angelo

Nature Communications, 2015, vol. 6, issue 1, 1-7

Abstract: Abstract The standard method for experimentally determining the probability distribution of an observable in quantum mechanics is the measurement of the observable spectrum. However, for infinite-dimensional degrees of freedom, this approach would require ideally infinite or, more realistically, a very large number of measurements. Here we consider an alternative method which can yield the mean and variance of an observable of an infinite-dimensional system by measuring only a two-dimensional pointer weakly coupled with the system. In our demonstrative implementation, we determine both the mean and the variance of the orbital angular momentum of a light beam without acquiring the entire spectrum, but measuring the Stokes parameters of the optical polarization (acting as pointer), after the beam has suffered a suitable spin–orbit weak interaction. This example can provide a paradigm for a new class of useful weak quantum measurements.

Date: 2015
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DOI: 10.1038/ncomms9606

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