Determination of weak values of quantum operators using only strong measurements

Eliahu Cohen and Eli Pollak
Phys. Rev. A 98, 042112 – Published 9 October 2018

Abstract

Weak values have been shown to be helpful especially when considering them as the outcomes of weak measurements. In this paper we show that, in principle, the real and imaginary parts of the weak value of any operator may be elucidated from expectation values of suitably defined density, flux, and Hermitian commutator operators. Expectation values are the outcomes of strong (projective) measurements, implying that weak values are general properties of operators in association with pre- and postselection and they need not be preferentially associated with weak measurements. They should be considered as an important measurable property which provides added information compared with the “standard” diagonal expectation value of an operator. As the first specific example we consider the determination of the real and imaginary parts of the weak value of the momentum operator employing projective time-of-flight experiments. Then the results are analyzed from the point of view of Bohmian mechanics. Finally, we consider recent neutron interferometry experiments used to determine the weak values of the neutron spin.

  • Received 14 May 2018
  • Revised 3 July 2018

DOI:https://doi.org/10.1103/PhysRevA.98.042112

©2018 American Physical Society

Physics Subject Headings (PhySH)

General Physics

Authors & Affiliations

Eliahu Cohen1,2 and Eli Pollak3,*

  • 1Physics Department, Centre for Research in Photonics, University of Ottawa, Advanced Research Complex, 25 Templeton, Ottawa, Ontario K1N 6N5, Canada
  • 2Faculty of Engineering and the Institute of Nanotechnology and Advanced Materials, Bar Ilan University, Ramat Gan 5290002, Israel
  • 3Chemical and Biological Physics Department, Weizmann Institute of Science, Rehovot 76100, Israel

  • *eli.pollak@weizmann.ac.il

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand
Issue

Vol. 98, Iss. 4 — October 2018

Reuse & Permissions
Access Options
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review A

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×