Nondeterministic quantum communication complexity: The cyclic equality game and iterated matrix multiplication

Publikation: Bidrag til bog/antologi/rapportKonferencebidrag i proceedingsForskningfagfællebedømt

Dokumenter

We study nondeterministic multiparty quantum communication with a quantum generalization of broadcasts. We show that, with number-in-hand classical inputs, the communication complexity of a Boolean function in this communication model equals the logarithm of the support rank of the corresponding tensor, whereas the approximation complexity in this model equals the logarithm of the border support rank. This characterisation allows us to prove a log-rank conjecture posed by Villagra et al. for nondeterministic multiparty quantum communication with message passing. The support rank characterization of the communication model connects quantum communication complexity intimately to the theory of asymptotic entanglement transformation and algebraic complexity theory. In this context, we introduce the graphwise equality problem. For a cycle graph, the complexity of this communication problem is closely related to the complexity of the computational problem of multiplying matrices, or more precisely, it equals the logarithm of the support rank of the iterated matrix multiplication tensor. We employ Strassen's laser method to show that asymptotically there exist nontrivial protocols for every odd-player cyclic equality problem. We exhibit an efficient protocol for the 5-player problem for small inputs, and we show how Young flattenings yield nontrivial complexity lower bounds.

OriginalsprogEngelsk
Titel8th Innovations in Theoretical Computer Science Conference, ITCS 2017
RedaktørerChristos H. Papadimitriou
ForlagSchloss Dagstuhl - Leibniz-Zentrum für Informatik
Publikationsdato2017
Sider1-18
Artikelnummer24
ISBN (Elektronisk)9783959770293
DOI
StatusUdgivet - 2017
Begivenhed8th Innovations in Theoretical Computer Science Conference, ITCS 2017 - Berkeley, USA
Varighed: 9 jan. 201711 jan. 2017

Konference

Konference8th Innovations in Theoretical Computer Science Conference, ITCS 2017
LandUSA
ByBerkeley
Periode09/01/201711/01/2017
SponsorSimons Institute for the Theory of Computing
NavnLeibniz International Proceedings in Informatics, LIPIcs
Vol/bind67
ISSN1868-8969

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