Why protective measurement does not establish the reality of the quantum state

  • Joshua Combes
  • Christopher Ferrie
  • Matthew S. Leifer
  • Matthew F. Pusey
Regular Paper


“Protective measurement” refers to two related schemes for finding the expectation value of an observable without disturbing the state of a quantum system, given a single copy of the system that is subject to a “protecting” operation. There have been several claims that these schemes support interpreting the quantum state as an objective property of a single quantum system. Here we provide three counter-arguments, each of which we present in two versions tailored to the two different schemes. Our first argument shows that the same resources used in protective measurement can be used to reconstruct the quantum state in a different way via process tomography. Our second argument is based on exact analyses of special cases of protective measurement, and our final argument is to construct explicit “\(\psi \)-epistemic” toy models for protective measurement, which strongly suggest that protective measurement does not imply the reality of the quantum state. The common theme of the three arguments is that almost all of the information comes from the “protection” operation rather than the quantum state of the system, and hence the schemes have no implications for the reality of the quantum state.


Ontological model Quantum measurement Protective measurement 



MP is grateful to Aharon Brodutch and Shan Gao for discussions, in particular to Shan for correcting MP’s initial misunderstanding of the Zeno scheme. Research at Perimeter Institute is supported in part by the Government of Canada through NSERC and by the Province of Ontario through MRI. CF was supported by NSF Grant No. PHY-1212445, the Canadian Government through the NSERC PDF program, the IARPA MQCO program, the ARC via EQuS Project Number CE11001013, and by the US Army Research Office Grant Numbers W911NF-14-1-0098 and W911NF-14-1-0103. ML is supported by the Foundational Questions Institute (FQXi). We would like to thank Paul Merriam for a careful proof reading.


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Copyright information

© Chapman University 2017

Authors and Affiliations

  1. 1.Institute for Quantum ComputingUniversity of WaterlooWaterlooCanada
  2. 2.Perimeter Institute for Theoretical PhysicsWaterlooCanada
  3. 3.Center for Quantum Information and ControlUniversity of New MexicoAlbuquerqueUSA
  4. 4.Centre for Engineered Quantum Systems, School of PhysicsUniversity of SydneySydneyAustralia

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