We give a tight lower bound of Omega(\sqrt{n}) for the randomized one-way communication complexity of the Boolean Hidden Matching Problem [BJK04]. Since there is a quantum one-way communication complexity protocol of O(log n) qubits for this problem, we obtain an exponential separation of quantum and classical one-way communication complexity for ... more >>>

We give the first exponential separation between quantum and bounded-error randomized one-way communication complexity. Specifically, we define the Hidden Matching Problem HM_n: Alice gets as input a string x in {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) ... more >>>

We prove exponential lower bounds on the length of 2-query
locally decodable codes. Goldreich et al. recently proved such bounds
for the special case of linear locally decodable codes.
Our proof shows that a 2-query locally decodable code can be decoded
with only 1 quantum query, and then ... more >>>