We give an exponential separation between one-way quantum and classical communication complexity for a Boolean function. Earlier such a separation was known only for a relation. A very similar result was obtained earlier but independently by Kerenidis and Raz [KR06]. Our version of the result gives an example in the ... more >>>

A strong direct product theorem says that if we want to compute k independent instances of a function, using less than k times the resources needed for one instance, then our overall success probability will be exponentially small in k. We establish such theorems for the classical as well as ... 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 proves an ... more >>>