Nondeterministic quantum communication complexity: The cyclic equality game and iterated matrix multiplication
Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review
Documents
- LIPIcs-ITCS-2017-24
Final published version, 545 KB, PDF document
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.
Original language | English |
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Title of host publication | 8th Innovations in Theoretical Computer Science Conference, ITCS 2017 |
Editors | Christos H. Papadimitriou |
Publisher | Schloss Dagstuhl - Leibniz-Zentrum für Informatik |
Publication date | 2017 |
Pages | 1-18 |
Article number | 24 |
ISBN (Electronic) | 9783959770293 |
DOIs | |
Publication status | Published - 2017 |
Event | 8th Innovations in Theoretical Computer Science Conference, ITCS 2017 - Berkeley, United States Duration: 9 Jan 2017 → 11 Jan 2017 |
Conference
Conference | 8th Innovations in Theoretical Computer Science Conference, ITCS 2017 |
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Land | United States |
By | Berkeley |
Periode | 09/01/2017 → 11/01/2017 |
Sponsor | Simons Institute for the Theory of Computing |
Series | Leibniz International Proceedings in Informatics, LIPIcs |
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Volume | 67 |
ISSN | 1868-8969 |
- Broadcast Channel, Matrix Multiplication, Number-Inhand, Quantum Communication Complexity, Support Rank
Research areas
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