Protective measurements: Extracting the expectation value by measuring a single particle

Fabrizio Piacentini*, Alessio Avella, Enrico Rebufello, Salvatore Virzì, Rudi Lussana, Federica Villa, Alberto Tosi, Marco Gramegna, Giorgio Brida, Eliahu Cohen, Lev Vaidman, Ivo Pietro Degiovanni, Marco Genovese

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


In quantum mechanics, the eigenvalues and their corresponding probabilities specify the expectation value of a physical observable, which is known to be a statistical property related to large ensembles of particles. In contrast to this paradigm, we demonstrate a unique method allowing to extract the expectation value of a single particle, namely, the polarisation of a single protected photon, with a single experiment. This is the first realisation of quantum protective measurements.

Original languageEnglish
Title of host publicationQuantum Technologies 2018
EditorsMiles J. Padgett, Andrew J. Shields, Jurgen Stuhler
ISBN (Electronic)9781510618749
StatePublished - 2018
EventQuantum Technologies 2018 - Strasbourg, France
Duration: 23 Apr 201825 Apr 2018

Publication series

NameProceedings of SPIE - The International Society for Optical Engineering
ISSN (Print)0277-786X
ISSN (Electronic)1996-756X


ConferenceQuantum Technologies 2018


  • expectation value
  • foundations of quantum mechanics
  • protective measurements
  • quantum metrology
  • quantum optics
  • single photons


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