Weizmann Logo
ECCC
Electronic Colloquium on Computational Complexity

Under the auspices of the Computational Complexity Foundation (CCF)

Login | Register | Classic Style



REPORTS > DETAIL:

Paper:

TR15-081 | 12th May 2015 17:55

Near-optimal bounds on bounded-round quantum communication complexity of disjointness

RSS-Feed

Abstract:

We prove a near optimal round-communication tradeoff for the two-party quantum communication complexity of disjointness. For protocols with $r$ rounds, we prove a lower bound of $\tilde{\Omega}(n/r)$ on the communication required for computing disjointness of input size $n$, which is optimal up to logarithmic factors. The previous best lower bound was $\Omega(n/r^2)$ due to Jain, Radhakrishnan and Sen. Along the way, we develop several tools for quantum information complexity, one of which is a lower bound for quantum information complexity in terms of the generalized discrepancy method. As a corollary, we get that the quantum communication complexity of any boolean function $f$ is at most $2^{O(QIC(f))}$, where $QIC(f)$ is the prior-free quantum information complexity of $f$ (with error $1/3$).



ISSN 1433-8092 | Imprint