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Colloquium: Understanding quantum weak values: Basics and applications

Justin Dressel, Mehul Malik, Filippo M. Miatto, Andrew N. Jordan, and Robert W. Boyd

Justin Dressel

  • Department of Physics and Astronomy and Center for Coherence and Quantum Optics, University of Rochester, Rochester, New York 14627, USA
  • and Department of Electrical Engineering, University of California, Riverside, California 92521, USA

Mehul Malik

  • The Institute of Optics, University of Rochester, Rochester, New York 14627, USA
  • and Institute for Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences, Boltzmanngasse 3, A-1090 Vienna, Austria

Filippo M. Miatto

  • Department of Physics, University of Ottawa, Ottawa, Ontario, Canada

Andrew N. Jordan

  • Department of Physics and Astronomy and Center for Coherence and Quantum Optics, University of Rochester, Rochester, New York 14627, USA

Robert W. Boyd

  • The Institute of Optics, University of Rochester, Rochester, New York 14627, USA
  • and Department of Physics, University of Ottawa, Ottawa, Ontario, Canada

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Rev. Mod. Phys. 86, 307 – Published 28 March, 2014

DOI: https://doi.org/10.1103/RevModPhys.86.307

Abstract

Since its introduction 25 years ago, the quantum weak value has gradually transitioned from a theoretical curiosity to a practical laboratory tool. While its utility is apparent in the recent explosion of weak value experiments, its interpretation has historically been a subject of confusion. Here a pragmatic introduction to the weak value in terms of measurable quantities is presented, along with an explanation for how it can be determined in the laboratory. Further, its application to three distinct experimental techniques is reviewed. First, as a large interaction parameter it can amplify small signals above technical background noise. Second, as a measurable complex value it enables novel techniques for direct quantum state and geometric phase determination. Third, as a conditioned average of generalized observable eigenvalues it provides a measurable window into nonclassical features of quantum mechanics. In this selective review, a single experimental configuration to discuss and clarify each of these applications is used.

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Rev. Mod. Phys. 86, 307– Published 28 March, 2014
  • Received 3 July 2013

© 2014 American Physical Society

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