Good Dynamics versus Bad Kinematics: Is Entanglement Needed for Quantum Computation?

Phys. Rev. Lett. 87, 047901 – Published 10 July 2001
Noah Linden and Sandu Popescu


We study the role of entanglement in quantum computation. We consider the case of a pure state contaminated by “white noise.” This framework arises, for example, in pseudopure state implementations of quantum computing using NMR. We analyze quantum computational protocols which aim to solve exponential classical problems with polynomial resources and ask whether or not entanglement of the pseudopure states is needed to achieve this aim. We show that, for a large class of such protocols, including Shor’s factorization, entanglement is necessary. We also show that achieving entanglement is not sufficient: If the state is sufficiently noisy, exponential resources are needed even if entanglement is present.


  • Received 24 June 1999
  • Published 10 July 2001

© 2001 The American Physical Society

Authors & Affiliations

Noah Linden1 and Sandu Popescu2

  • 1Department of Mathematics, University of Bristol, University Walk, Bristol BS8 1TW, United Kingdom
  • 2HH Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol BS8 1TL, United Kingdom and BRIMS, Hewlett-Packard Laboratories, Stoke Gifford, Bristol BS12 6QZ, United Kingdom

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