Lower bounds for quantum communication complexity
Abstract
We prove new lower bounds for bounded error quantum communication complexity. Our methods are based on the Fourier transform of the considered functions. First we generalize a method for proving classical communication complexity lower bounds developed by Raz to the quantum case. Applying this method we give an exponential separation between bounded error quantum communication complexity and nondeterministic quantum communication complexity. We develop several other lower bound methods based on the Fourier transform, notably showing that \sqrt{\bar{s}(f)/\log n}, for the average sensitivity \bar{s}(f) of a function f, yields a lower bound on the bounded error quantum communication complexity of f(x AND y XOR z), where x is a Boolean word held by Alice and y,z are Boolean words held by Bob. We then prove the first large lower bounds on the bounded error quantum communication complexity of functions, for which a polynomial quantum speedup is possible. For all the functions we investigate, the only previously applied general lower bound method based on discrepancy yields bounds that are O(\log n).
 Publication:

arXiv eprints
 Pub Date:
 June 2001
 arXiv:
 arXiv:quantph/0106160
 Bibcode:
 2001quant.ph..6160K
 Keywords:

 Quantum Physics
 EPrint:
 26pages, appeared in the Proceedings of the 42nd IEEE Symposium on Foundations of Computer Science