Role of entanglement and correlations in mixed-state quantum computation

Animesh Datta and Guifre Vidal
Phys. Rev. A 75, 042310 – Published 11 April 2007

Abstract

In a quantum computation with pure states, the generation of large amounts of entanglement is known to be necessary for a speedup with respect to classical computations. However, examples of quantum computations with mixed states are known, such as the deterministic computation with one quantum qubit (DQC1) model [Knill and Laflamme, Phys. Rev. Lett. 81, 5672 (1998)], in which entanglement is at most marginally present, and yet a computational speedup is believed to occur. Correlations, and not entanglement, have been identified as a necessary ingredient for mixed-state quantum computation speedups. Here we show that correlations, as measured through the operator Schmidt rank, are indeed present in large amounts in the DQC1 circuit. This provides evidence for the preclusion of efficient classical simulation of DQC1 by means of a whole class of classical simulation algorithms, thereby reinforcing the conjecture that DQC1 leads to a genuine quantum computational speedup.

  • Figure
  • Received 14 November 2006

DOI:https://doi.org/10.1103/PhysRevA.75.042310

©2007 American Physical Society

Authors & Affiliations

Animesh Datta*

  • Department of Physics and Astronomy, University of New Mexico, Albuquerque, New Mexico 87131-1156, USA

Guifre Vidal

  • School of Physical Sciences, The University of Queensland, Queensland 4072, Australia

  • *Electronic address: animesh@unm.edu
  • Electronic address: vidal@physics.uq.edu.au

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Issue

Vol. 75, Iss. 4 — April 2007

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