Complexity of Causal Order Structure in Distributed Quantum Information Processing: More Rounds of Classical Communication Reduce Entanglement Cost

Eyuri Wakakuwa, Akihito Soeda, and Mio Murao
Phys. Rev. Lett. 122, 190502 – Published 16 May 2019
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Abstract

We prove a trade-off relation between the entanglement cost and classical communication round complexity of a protocol in implementing a class of two-qubit unitary gates by two distant parties, a key subroutine in distributed quantum information processing. The task is analyzed in an information theoretic scenario of asymptotically many input pairs with a small error that is required to vanish sufficiently quickly. The trade-off relation is shown by (i) one ebit of entanglement per pair is necessary for implementing the unitary by any two-round protocol, and (ii) the entanglement cost by a three-round protocol is strictly smaller than one ebit per pair. We also provide an example of bipartite unitary gates for which there is no such trade-off.

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  • Received 22 October 2018

DOI:https://doi.org/10.1103/PhysRevLett.122.190502

© 2019 American Physical Society

Physics Subject Headings (PhySH)

Quantum Information, Science & Technology

Authors & Affiliations

Eyuri Wakakuwa1,2,*, Akihito Soeda3, and Mio Murao3,4

  • 1Department of Communication Engineering and Informatics, Graduate School of Informatics and Engineering, The University of Electro-Communications, 1-5-1 Chofugaoka, Chofu-shi, Tokyo 182-8585, Japan
  • 2Department of Complexity Science and Engineering, Graduate School of Frontier Sciences, The University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa-shi, Chiba 277-0882, Japan
  • 3Department of Physics, Graduate School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
  • 4Institute for Nano Quantum Information Electronics, The University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8505, Japan

  • *wakakuwa@quest.is.uec.ac.jp

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Issue

Vol. 122, Iss. 19 — 17 May 2019

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