Quantum Communication Cannot Simulate a Public Coin
Abstract
We study the simultaneous message passing model of communication complexity. Building on the quantum fingerprinting protocol of Buhrman et al., Yao recently showed that a large class of efficient classical publiccoin protocols can be turned into efficient quantum protocols without public coin. This raises the question whether this can be done always, i.e. whether quantum communication can always replace a public coin in the SMP model. We answer this question in the negative, exhibiting a communication problem where classical communication with public coin is exponentially more efficient than quantum communication. Together with a separation in the other direction due to BarYossef et al., this shows that the quantum SMP model is incomparable with the classical publiccoin SMP model. In addition we give a characterization of the power of quantum fingerprinting by means of a connection to geometrical tools from machine learning, a quadratic improvement of Yao's simulation, and a nearly tight analysis of the Hamming distance problem from Yao's paper.
 Publication:

arXiv eprints
 Pub Date:
 November 2004
 arXiv:
 arXiv:quantph/0411051
 Bibcode:
 2004quant.ph.11051G
 Keywords:

 Quantum Physics;
 Computer Science  Computational Complexity
 EPrint:
 12 pages LaTeX