Quantum multi-prover interactive proof systems with limited prior entanglement

  • Authors:

  • Hirotada Kobayashi;Keiji Matsumoto

  • Affiliations:

  • Quantum Computation and Information Project, Exploratory Research for Advanced Technology, Japan Sci. and Tech. Corp. and Dept. of Info. Sci., Graduate School of Science, The University of Tokyo, ...;Quantum Computation and Information Project, Exploratory Research for Advanced Technology, Japan Science and Technology Corporation, 5-28-3 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan

  • Venue:
  • Journal of Computer and System Sciences
  • Year:
  • 2003

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Abstract

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.