We prove that the concept class of disjunctions cannot be pointwise approximated by linear combinations of any small set of arbitrary real-valued functions. That is, suppose that t...
We show a tight lower bound of Ω(N log log N) on the number of transmissions required to compute several functions (including the parity function and the majority function) in a...
We give a tight lower bound of ( n) for the randomized one-way communication complexity of the Boolean Hidden Matching Problem [BJK04]. Since there is a quantum one-way communica...
A strong direct product theorem (SDPT) states that solving n instances of a problem requires ˝.n/ times the resources for a single instance, even to achieve success probability 2 ...
We present two general methods for proving lower bounds on the query complexity of nonadaptive quantum algorithms. Both methods are based on the adversary method of Ambainis. We sh...