Theory and experiment for resource-efficient joint weak-measurement

Author:

Martinez-Becerril Aldo C.1,Bussières Gabriel1,Curic Davor2,Giner Lambert13,A. Abrahao Raphael14,Lundeen Jeff S.14

Affiliation:

1. Department of Physics and Centre for Research in Photonics, University of Ottawa, 25 Templeton Street, Ottawa, Ontario K1N 6N5, Canada

2. Complexity Science Group, Department of Physics and Astronomy, University of Calgary, 2500 University Drive NW, Calgary, Alberta, Canada T2N 1N4

3. Département de Physique et d’Astronomie, Université de Moncton, 18 Ave. Antonine-Maillet, Moncton, New Brunswick E1A 3E9, Canada

4. Joint Centre for Extreme Photonics, University of Ottawa - National Research Council of Canada, 100 Sussex Drive, Ottawa, Ontario K1A 0R6, Canada

Abstract

Incompatible observables underlie pillars of quantum physics such as contextuality and entanglement. The Heisenberg uncertainty principle is a fundamental limitation on the measurement of the product of incompatible observables, a 'joint' measurement. However, recently a method using weak measurement has experimentally demonstrated joint measurement. This method [Lundeen, J. S., and Bamber, C. Phys. Rev. Lett. 108, 070402, 2012] delivers the standard expectation value of the product of observables, even if they are incompatible. A drawback of this method is that it requires coupling each observable to a distinct degree of freedom (DOF), i.e., a disjoint Hilbert space. Typically, this 'read-out' system is an unused internal DOF of the measured particle. Unfortunately, one quickly runs out of internal DOFs, which limits the number of observables and types of measurements one can make. To address this limitation, we propose and experimentally demonstrate a technique to perform a joint weak-measurement of two incompatible observables using only one DOF as a read-out system. We apply our scheme to directly measure the density matrix of photon polarization states.

Publisher

Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften

Subject

Physics and Astronomy (miscellaneous),Atomic and Molecular Physics, and Optics

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