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.

Directly measuring mean and variance of infinite-spectrum observables such as the photon orbital angular momentum / Piccirillo, Bruno; Slussarenko, Sergei; Marrucci, Lorenzo; Santamato, Enrico. - In: NATURE COMMUNICATIONS. - ISSN 2041-1723. - 6:(2015), p. 8606. [10.1038/ncomms9606]

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

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.
2015
Directly measuring mean and variance of infinite-spectrum observables such as the photon orbital angular momentum / Piccirillo, Bruno; Slussarenko, Sergei; Marrucci, Lorenzo; Santamato, Enrico. - In: NATURE COMMUNICATIONS. - ISSN 2041-1723. - 6:(2015), p. 8606. [10.1038/ncomms9606]
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11588/613709
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 13
  • ???jsp.display-item.citation.isi??? 13
social impact