International Journal of Theoretical Physics

, Volume 56, Issue 1, pp 232–258 | Cite as

How to Measure the Quantum Measure

In memory of David Ritz Finkelstein
  • Álvaro Mozota Frauca
  • Rafael Dolnick Sorkin


The histories-based framework of Quantum Measure Theory assigns a generalized probability or measure μ(E) to every (suitably regular) set E of histories. Even though μ(E) cannot in general be interpreted as the expectation value of a selfadjoint operator (or POVM), we describe an arrangement which makes it possible to determine μ(E) experimentally for any desired E. Taking, for simplicity, the system in question to be a particle passing through a series of Stern-Gerlach devices or beam-splitters, we show how to couple a set of ancillas to it, and then to perform on them a suitable unitary transformation followed by a final measurement, such that the probability of a final outcome of “yes” is related to μ(E) by a known factor of proportionality. Finally, we discuss in what sense a positive outcome of the final measurement should count as a minimally disturbing verification that the microscopic event E actually happened.


Quantum measure theory Coupling ancillas 



AMF would like to thank his PSI partners for their useful discussions and the long hours working together. This research was supported in part by NSERC through grant RGPIN-418709-2012. This research was supported in part by Perimeter Institute for Theoretical Physics. Research at Perimeter Institute is supported by the Government of Canada through Industry Canada and by the Province of Ontario through the Ministry of Economic Development and Innovation.


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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  • Álvaro Mozota Frauca
    • 1
  • Rafael Dolnick Sorkin
    • 1
    • 2
  1. 1.Perimeter Institute for Theoretical PhysicsWaterlooCanada
  2. 2.Department of PhysicsSyracuse UniversitySyracuseUSA

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