  This paper gives the first formal treatment of a quantum analogue of
multi-prover interactive proof systems. It is proved that the class of
languages having quantum multi-prover interactive proof systems is necessarily
contained in NEXP, under the assumption that provers are allowed to share at
most polynomially many prior-entangled qubits. This implies that, in
particular, if provers do not share any prior entanglement with each other, the
class of languages having quantum multi-prover interactive proof systems is
equal to NEXP. Related to these, it is shown that, in the case a prover does
not have his private qubits, the class of languages having quantum
single-prover interactive proof systems is also equal to NEXP.
