The quantum communication complexity of the pointer chasing problem: The bit version

Abstract

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 Zuck-erman [7]. We show that in any quantum protocol for this problem, the two players must exchange Ω (n/k4) qubits. This improves the previous best lower bound of Ω (n/22O(k)) in [7], and comes significantly closer to the best upper bounds known: O(n + k logn) (classical deterministic [12]) and O(klogn+n/k(log(k/2) 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