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

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 the...

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Bibliographic Details
Published in:Physical review letters 2019-05, Vol.122 (19), p.190502-190502, Article 190502
Main Authors: Wakakuwa, Eyuri, Soeda, Akihito, Murao, Mio
Format: Article
Language:English
Subjects:
Complexity
Data processing
Information processing
Information theory
Quantum entanglement
Quantum phenomena
Qubits (quantum computing)
Tradeoffs
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Summary: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.
ISSN:0031-9007
1079-7114
DOI:10.1103/physrevlett.122.190502