On the Power of Quantum Proofs

We study the power of quantum proofs, or more precisely, the power of Quantum MerlinArthur (QMA) protocols, in two well studied models of quantum computation: the black box model and the communication complexity model. Our main results are obtained for the communication complexity model. For this model, we identify a complete promise problem for QMA protocols, the Linear Subspaces Distance problem. The problem is of geometrical nature: Each player gets a linear subspace of Rm and considers the sphere of unit vectors in that subspace. Their goal is to output 1 if the distance between the two spheres is very small (say, smaller than 0.1 · √ 2) and 0 if the distance is very large (say, larger than 0.9 · √ 2). We show that:

• Type: Conference
• Year: 2004
• Where: COCO
• Authors: Ran Raz, Amir Shpilka
• Keywords: COCO 2004, Communication Complexity Model, Linear Subspace, Linear Subspaces Distance