Article

# Interaction in Quantum Communication and the Complexity of Set Disjointness

10/2001;
Source: DBLP

ABSTRACT One of the most intriguing facts about communication using quantum states is that these states cannot be used to transmit more classical bits than the number of qubits used, yet in some scenarios there are ways of conveying information with much fewer, even exponentially fewer, qubits than possible classically [1], [2], [3]. Moreover, some of these methods have a very simple structure|they involve only few message exchanges between the communicating parties. We consider the question as to whether every classical protocol may be transformed to a simpler" quantum protocol|one that has similar eciency, but uses fewer message exchanges.

0 0
·
0 Bookmarks
·
50 Views
• Source
##### Article: A lower bound for bounded round quantum communication complexity of set disjointness
[hide abstract]
ABSTRACT: We consider the class of functions whose value depends only on the intersection of the input X_1,X_2, ..., X_t; that is, for each F in this class there is an f_F: 2^{[n]} \to {0,1}, such that F(X_1,X_2, ..., X_t) = f_F(X_1 \cap X_2 \cap ... \cap X_t). We show that the t-party k-round communication complexity of F is Omega(s_m(f_F)/(k^2)), where s_m(f_F) stands for the `monotone sensitivity of f_F' and is defined by s_m(f_F) \defeq max_{S\subseteq [n]} |{i: f_F(S \cup {i}) \neq f_F(S)|. For two-party quantum communication protocols for the set disjointness problem, this implies that the two parties must exchange Omega(n/k^2) qubits. For k=1, our lower bound matches the Omega(n) lower bound observed by Buhrman and de Wolf (based on a result of Nayak, and for 2 <= k <= n^{1/4}, improves the lower bound of Omega(sqrt{n}) shown by Razborov. (For protocols with no restrictions on the number of rounds, we can conclude that the two parties must exchange Omega(n^{1/3}) qubits. This, however, falls short of the optimal Omega(sqrt{n}) lower bound shown by Razborov.)
04/2003;
• ##### Conference Proceeding: Rounds in Communication Complexity Revisited
[hide abstract]
ABSTRACT: The k-round two-party communication complexity was studied in the deterministic model by (14) and (4) and in the probabilistic model by (20) and (6). We present new lower bounds that give (1) randomization is more powerful than determinism in k-round protocols, and (2) an explicit function which exhibits an exponential gap between its k and (k 1)-round randomized complexity. We also study the three party communication model, and exhibit an exponential gap in 3-round protocols that dier in the starting player. Finally, we show new connections of these questions to circuit complexity, that motivate further work in this direction.
Proceedings of the 23rd Annual ACM Symposium on Theory of Computing, May 5-8, 1991, New Orleans, Louisiana, USA; 01/1991
• ##### Conference Proceeding: The Communication Complexity of Pointer Chasing Applications of Entropy and Sampling (Abstract).
Proceedings of the Thirty-First Annual ACM Symposium on Theory of Computing, May 1-4, 1999, Atlanta, Georgia, USA; 01/1999