Weak Measurements Are Universal

Ognyan Oreshkov and Todd A. Brun
Phys. Rev. Lett. 95, 110409 – Published 9 September 2005

Abstract

It is well known that any projective measurement can be decomposed into a sequence of weak measurements, which cause only small changes to the state. Similar constructions for generalized measurements, however, have relied on the use of an ancilla system. We show that any generalized measurement can be decomposed into a sequence of weak measurements without the use of an ancilla, and give an explicit construction for these weak measurements. The measurement procedure has the structure of a random walk along a curve in state space, with the measurement ending when one of the end points is reached. This shows that any measurement can be generated by weak measurements, and hence that weak measurements are universal. This may have important applications to the theory of entanglement.

  • Received 2 March 2005

DOI:https://doi.org/10.1103/PhysRevLett.95.110409

©2005 American Physical Society

Authors & Affiliations

Ognyan Oreshkov*

  • Department of Physics, University of Southern California, Los Angeles, California 90089, USA

Todd A. Brun

  • Communication Sciences Institute, University of Southern California, Los Angeles, California 90089, USA

  • *Electronic address: oreshkov@usc.edu
  • Electronic address: tbrun@usc.edu

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Vol. 95, Iss. 11 — 9 September 2005

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