Exponential separation of quantum and classical one-way communication complexity

Abstract. We give the first exponential separation between quantum and bounded-error randomized one-way communication complexity. Specifically, we define the Hidden Matching Problem HMn: Alice gets as input a string x {0, 1}n and Bob gets a perfect matching M on the n coordinates. Bob's goal is to output a tuple i, j, b such that the edge (i, j) belongs to the matching M and b = xi xj. We prove that the quantum one-way communication complexity of HMn is O(log n), yet any randomized one-way protocol with bounded error must use ( n) bits of communication. No asymptotic gap for one-way communication was previously known. Our bounds also hold in the model of Simultaneous Messages (SM) and hence we provide the first exponential separation between quantum SM and randomized SM with public coins. For a Boolean decision version of HMn, we show that the quantum one-way communication complexity remains O(log n) and that the 0-error randomized one-way communication complexity is (n). We pr...

• Type: Conference
• Year: 2004
• Where: STOC
• Authors: Ziv Bar-Yossef, T. S. Jayram, Iordanis Kerenidis
• Keywords: Algorithms, One-way Communication Complexity, Quantum One-way Communication, Randomized One-way Protocol, STOC 2004