Quantum Multi-Prover Interactive Proof Systems with Limited Prior Entanglement

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.