Abstract. In recent years we have witnessed the proliferation of semidefinite programming bounds in combinatorial optimization [1,5,8], quantum computing [9,2,3,6,4,16] and even in complexity theory [7,17,18]. Examples to such bounds include the semidefinite relaxation for the maximal cut problem [5], and the quantum value of multi-prover interactive games [3,4,16]. The first semidefinite programming bound, which gained fame, arose in the late seventies and was due to L