Coherence as a resource in decision problems: The Deutsch-Jozsa algorithm and a variation

Mark Hillery
Phys. Rev. A 93, 012111 – Published 13 January 2016

Abstract

That superpositions of states can be useful for performing tasks in quantum systems has been known since the early days of quantum information, but only recently has a quantitative theory of quantum coherence been proposed. Here we apply that theory to an analysis of the Deutsch-Jozsa algorithm, which depends on quantum coherence for its operation. The Deutsch-Jozsa algorithm solves a decision problem, and we focus on a probabilistic version of that problem, comparing probability of being correct for both classical and quantum procedures. In addition, we study a related decision problem in which the quantum procedure has one-sided error while the classical procedure has two-sided error. The role of coherence on the quantum success probabilities in both of these problems is examined.

  • Figure
  • Received 8 September 2015

DOI:https://doi.org/10.1103/PhysRevA.93.012111

©2016 American Physical Society

Physics Subject Headings (PhySH)

Quantum Information, Science & Technology

Authors & Affiliations

Mark Hillery

  • Department of Physics, Hunter College of the City University of New York, 695 Park Avenue, New York, New York 10065, USA
  • and Physics Program, Graduate Center of the City University of New York, 365 Fifth Avenue, New York, New York 10016, USA

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Issue

Vol. 93, Iss. 1 — January 2016

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