This paper studies whether quantum proofs are more powerful than
classical proofs, or in complexity terms, whether QMA=QCMA. We prove
two results about this question. First, we give a "quantum oracle
separation" between QMA and QCMA. More concretely, we show that any
quantum algorithm needs order sqrt(2^n/(m+1)) queries to find ... more >>>

We define tests of boolean functions which
distinguish between linear (or quadratic) polynomials, and functions
which are very far, in an appropriate sense, from these
polynomials. The tests have optimal or nearly optimal trade-offs
between soundness and the number of queries.

In particular, we show that functions with small ... more >>>

A coloring of a graph is {\it convex} if it
induces a partition of the vertices into connected subgraphs.
Besides being an interesting property from a theoretical point of
view, tests for convexity have applications in various areas
involving large graphs. Our results concern the important subcase
of testing for ... more >>>