Lower bounds on communication complexity
Information and Computation
Elements of information theory
Elements of information theory
Rounds in communication complexity revisited
SIAM Journal on Computing
Quantum circuits with mixed states
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
On data structures and asymmetric communication complexity
Journal of Computer and System Sciences
On quantum and probabilistic communication: Las Vegas and one-way protocols
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
The communication complexity of pointer chasing
Journal of Computer and System Sciences - Special issue on the fourteenth annual IEE conference on computational complexity
Interaction in quantum communication and the complexity of set disjointness
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Quantum computation and quantum information
Quantum computation and quantum information
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Lower Bounds in the Quantum Cell Probe Model
ICALP '01 Proceedings of the 28th International Colloquium on Automata, Languages and Programming,
The Quantum Communication Complexity of Sampling
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
SFCS '93 Proceedings of the 1993 IEEE 34th Annual Foundations of Computer Science
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We consider the two-party quantum communication complexity of the bit version of the pointer chasing problem when the 'wrong' player starts, originally studied by Klauck, Nayak, Ta-Shma and Zuckerman [7]. We show that in any quantum protocol for this problem, the two players must exchange 驴(n/k4) qubits. This improves the previous best lower bound of 驴(n/22O(k)) in [7], and comes significantly closer to the best upper bounds known: O(n + k log n) (classical deterministic [12]) and O(k log n + n/k (log(驴 k/2驴) n+log k)) (classical randomised [7]). Our result demonstrates a separation between the communication complexity of k and k - 1 round bounded error quantum protocols, for all k O((m/log2 m)1/5), where m is the size of the inputs to Alice and Bob. Earlier works could prove such a separation for much smaller k only. Our proof uses a round elimination argument for a class of quantum sampling protocols with correlated input generation, making better use of information-theoretic tools than previous works.