Optimal Pure-State Qubit Tomography via Sequential Weak Measurements

Ezad Shojaee, Christopher S. Jackson, Carlos A. Riofrío, Amir Kalev, and Ivan H. Deutsch
Phys. Rev. Lett. 121, 130404 – Published 26 September 2018

Abstract

The spin-coherent-state positive-operator-valued-measure (POVM) is a fundamental measurement in quantum science, with applications including tomography, metrology, teleportation, benchmarking, and measurement of Husimi phase space probabilities. We prove that this POVM is achieved by collectively measuring the spin projection of an ensemble of qubits weakly and isotropically. We apply this in the context of optimal tomography of pure qubits. We show numerically that through a sequence of weak measurements of random directions of the collective spin component, sampled discretely or in a continuous measurement with random controls, one can approach the optimal bound.

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  • Received 9 May 2018

DOI:https://doi.org/10.1103/PhysRevLett.121.130404

© 2018 American Physical Society

Physics Subject Headings (PhySH)

Quantum Information, Science & Technology

Authors & Affiliations

Ezad Shojaee1, Christopher S. Jackson1, Carlos A. Riofrío2, Amir Kalev3, and Ivan H. Deutsch1

  • 1Center for Quantum Information and Control (CQuIC) Department of Physics and Astronomy, University of New Mexico, Albuquerque, New Mexico 87131, USA
  • 2Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, Berlin, Germany
  • 3Joint Center for Quantum Information and Computer Science (QuICS), University of Maryland, College Park, Maryland 20742, USA

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Issue

Vol. 121, Iss. 13 — 28 September 2018

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