Hostname: page-component-78c5997874-t5tsf Total loading time: 0 Render date: 2024-11-05T03:19:26.957Z Has data issue: false hasContentIssue false
  • English
  • Français

Quantum multiparty communication complexity and circuit lower bounds

Published online by Cambridge University Press:  01 February 2009

IORDANIS KERENIDIS
IORDANIS KERENIDIS*
Affiliation:
CNRS, LRI-Université de Paris-Sud, Paris, France Email: jkeren@lri.fr
Get access Rights & Permissions [Opens in a new window]

Abstract

We define a quantum model for multiparty communication complexity and prove a simulation theorem between the classical and quantum models. As a result, we show that if the quantum k-party communication complexity of a function f is Ω(n/2k), its classical k-party communication is Ω(n/2k/2). Finding such an f would allow us to prove strong classical lower bounds for k ≥ log n players and make progress towards solving a major open question about symmetric circuits.

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 19 , Special Issue 1: Theory and Applications of Models of Computation (TAMC) , February 2009 , pp. 119 - 132
Copyright
Copyright © Cambridge University Press 2009

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Aaronson, S. (2004) Lower bounds for local search by quantum arguments. In: Proceedings of 36th ACM STOC.CrossRefGoogle Scholar
Aaronson, S. (2005) Quantum Computing, Postselection, and Probabilistic Polynomial-Time. In: Proceedings of the Royal Society A 461 (2063)3473–3482.CrossRefGoogle Scholar
Aharonov, D. and Regev, O. (2003) A Lattice Problem in Quantum NP. In: Proc. 44th IEEE FOCS.Google Scholar
Aharonov, D. and Regev, O. (2004) Lattice problems in NP ∩ coNP. In: Proc. 45th IEEE FOCS.Google Scholar
Babai, L., Nisan, N. and Szegedy, M. (1992) Multiparty protocols, pseudorandom generators for logspace, and time-space trade-offs. Journal of Computer and System Sciences 45 (2)204–232.CrossRefGoogle Scholar
Bar-Yossef, Z., Jayram, T. S. and Kerenidis, I. (2004) Exponential Separation of Quantum and Classical One-Way Communication Complexity. Proceedings of 36th ACM STOC.CrossRefGoogle Scholar
Beigel, R. and Tarui, J. (1994) On ACC. Computational Complexity 4 (4)350–366.CrossRefGoogle Scholar
Buhrman, H., Cleve, R., Watrous, J. and de Wolf, R. (2001) Quantum fingerprinting. Physical Review Letters 87 (16).CrossRefGoogle ScholarPubMed
Chandra, A. K., Furst, M. L. and Lipton, R. J. (1983) Multi-party protocols. In: Proceedings of the 15th annual ACM STOC.CrossRefGoogle Scholar
Chung, F. (1990) Quasi-random classes of hypergraphs. Random Structures and Algorithms 1 (4)363–382.CrossRefGoogle Scholar
Gavinsky, D., Kempe, J., Kerenidis, I., Raz, R. and de Wolf, R. (2007) Exponential separations for one-way quantum communication complexity, with applications to cryptography. Proceedings of ACM STOC.CrossRefGoogle Scholar
Grolmusz, V. (1994) The BNS Lower Bound for Multi-Party Protocols is Nearly Optimal. Information and Computation 112 (1)51–54.CrossRefGoogle Scholar
Hastad, J. and Goldmann, M. (1991) On the power of small-depth threshold circuits. Computational Complexity 1 113–129.CrossRefGoogle Scholar
Kerenidis, I. and de Wolf, R. (2003) Exponential Lower Bound for 2-Query Locally Decodable Codes via a Quantum Argument. In: Proceedings of the 15th annual ACM STOC.CrossRefGoogle Scholar
Kushilevitz, E. and Nisan, N. (1997) Communication complexity, Cambridge University Press.Google Scholar
Nielsen, M. and Chuang, I.. (2000) Quantum Computation and Quantum Information, Cambridge University Press.Google Scholar
Raz, R. (1999) Exponential separation of quantum and classical communication complexity. In: Proceedings of 31st ACM STOC.CrossRefGoogle Scholar
Raz, R. (2000) The BNS-Chung Criterion for multi-party communication complexity. Journal of Computational Complexity 9 (2)113–122.CrossRefGoogle Scholar
Wehner, S. and de Wolf, R. (2005) Improved Lower Bounds for Locally Decodable Codes and Private Information Retrieval. In 32nd ICALP. Springer-Verlag Lecture Notes in Computer Science 3580 1424–1436.CrossRefGoogle Scholar
de Wolf, R. (2005) Lower Bounds on Matrix Rigidity via a Quantum Argument. In: 33rd International Colloquium on Automata, Languages and Programming (ICALP'06). Springer-Verlag Lecture Notes in Computer Science 4051 62–71.CrossRefGoogle Scholar
Yao, A. C. (1990) On ACC and threshold circuits. In: Proc. 31st Ann. IEEE FOCS.Google Scholar