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.Comment: LaTeX2e, 19 pages, 2 figures, title changed, some of the sections are fully revised, journal version in Journal of Computer and System Science

Entanglement-Resistant Two-Prover Interactive Proof Systems and Non-Adaptive Private Information Retrieval Systems

We show that, for any language in NP, there is an entanglement-resistant constant-bit two-prover interactive proof system with a constant completeness vs. soundness gap. The previously proposed classical two-prover constant-bit interactive proof systems are known not to be entanglement-resistant. This is currently the strongest expressive power of any known constant-bit answer multi-prover interactive proof system that achieves a constant gap. Our result is based on an "oracularizing" property of certain private information retrieval systems, which may be of independent interest.Comment: 8 page

On the power of quantum, one round, two prover interactive proof systems

We analyze quantum two prover one round interactive proof systems, in which noninteracting provers can share unlimited entanglement. The maximum acceptance probability is characterized as a superoperator norm. We get some partial results about the superoperator norm, and in particular we analyze the "rank one" case.Comment: 12 pages, no figure

On quantum interactive proofs with short messages

This paper proves one of the open problem posed by Beigi et al. in arXiv:1004.0411v2. We consider quantum interactive proof systems where in the beginning the verifier and prover send messages to each other with the combined length of all messages being at most logarithmic (in the input length); and at the end the prover sends a polynomial-length message to the verifier. We show that this class has the same expressive power as QMA.Comment: 9 pages, 3 figure

On the power quantum computation over real Hilbert spaces

We consider the power of various quantum complexity classes with the restriction that states and operators are defined over a real, rather than complex, Hilbert space. It is well know that a quantum circuit over the complex numbers can be transformed into a quantum circuit over the real numbers with the addition of a single qubit. This implies that BQP retains its power when restricted to using states and operations over the reals. We show that the same is true for QMA(k), QIP(k), QMIP, and QSZK.Comment: Significant improvements from previous version, in particular showing both containments (eg. QMA_R is in QMA and vice versa