Entangled and Sequential Quantum Protocols with Dephasing

Sergio Boixo and Chris Heunen
Phys. Rev. Lett. 108, 120402 – Published 21 March 2012
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Abstract

Sequences of commuting quantum operators can be parallelized using entanglement. This transformation is behind some optimal quantum metrology protocols and recent results on quantum circuit complexity. We show that dephasing quantum maps in arbitrary dimension can also be parallelized. This implies that for general dephasing noise the protocol with entanglement is not more fragile than the corresponding sequential protocol and, conversely, the sequential protocol is not less effective than the entangled one. We derive this result using tensor networks. Furthermore, we only use transformations strictly valid within string diagrams in dagger compact closed categories. Therefore, they apply verbatim to other theories, such as geometric quantization and topological quantum field theory. This clarifies and characterizes to some extent the role of entanglement in general quantum theories.

  • Received 23 August 2011

DOI:http://dx.doi.org/10.1103/PhysRevLett.108.120402

© 2012 American Physical Society

Authors & Affiliations

Sergio Boixo1 and Chris Heunen2

  • 1Department of Chemistry and Chemical Biology, Harvard University, Cambridge, Massachusetts 02138, USA
  • 2Department of Computer Science, Oxford University, Wolfson Building, Parks Road, Oxford OX1 3QD, United Kingdom

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Vol. 108, Iss. 12 — 23 March 2012

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