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

Eyuri Wakakuwa; Akihito Soeda; Mio Murao

doi:10.1103/PhysRevLett.122.190502

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

Phys Rev Lett. 2019 May 17;122(19):190502. doi: 10.1103/PhysRevLett.122.190502.

Authors

Eyuri Wakakuwa^{1

2}, Akihito Soeda³, Mio Murao^{3

4}

Affiliations

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

PMID: 31144967
DOI: 10.1103/PhysRevLett.122.190502

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.