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

Piccirillo, Bruno, Slussarenko, Sergei, Marrucci, Lorenzo, Santamato, Enrico·2015·Nature Communications
DOI 10.1038/ncomms9606PMC PMC4634339
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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.

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  • OAM has enabled optimal quantum cloning of OAM-encoded qubits and photonic quantum walks in OAM states, with theoretical analyses and experimental demonstrations.

    “At a fundamental level, OAM has enabled researches on optimal quantum cloning of OAM-encoded qubits [66,81] and photonic quantum walks in the orbital angular momentum states, with theoretical analyses [82,83] and experimental demonstrations [51,54,60].”

    From Photonic quantum information processing: a review (2019) · cites this paper as [83]

    The Results (Experimental demonstration; page unavailable) describe measurements of the moments of OAM superpositions, not cloning or photonic quantum walks. The Discussion (page unavailable) identifies the demonstration as a classical-optics experiment. Searches for quantum walks and cloning found no passage addressing the research attributed to this source. (LLM, conf=0.76)

    Experimental — accuracy not yet measured

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Research works printed but not linked: 35

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Metadata

Authors
Piccirillo, B., Slussarenko, S., Marrucci, L., & Santamato, E.
Venue
Nature Communications
Publisher
Springer Science and Business Media LLC
Published
2015-10-19
Volume
6
Issue
1
ISSN
2041-1723
DOI
10.1038/ncomms9606
PMC
PMC4634339
Cited by
16
References
1
Language
en
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