Quantum Information Processing, Vol. 6, No. 6, December 2007 (© 2007)
On the Power of Quantum, One Round, Two Prover
Interactive Proof Systems
and Amnon Ta-Shma
Received June 21, 2007; accepted September 23, 2007; Published online: November 17, 2007
We analyze quantum two prover one round interactive proof systems, in which
noninteracting provers can share unlimited entanglement. The maximum accep-
tance probability is characterized as a superoperator norm. We get some partial
results and in particular we analyze the “rank one” case.
KEY WORDS: quantum interactive proofs; non-local games; diamond norm;
PACS: 03.67.Lx; 03.65.Ud; 03.67.Ac.
Classical interactive proof systems allow an interaction between an efﬁ-
cient veriﬁer and an all powerful prover. Classical interactive proof sys-
tems are quite powerful: one prover can prove theorems in PSPACE to
an efﬁcient veriﬁer
while two or more powerful provers that cannot
interact between themselves can prove the whole of NEXP.
Kitaev and Watrous
studied the power of interaction between an
efﬁcient quantum veriﬁer and a single prover. They prove that such a
proof system is at least as powerful as a classical one prover proof system
but probably not as powerful as classical two provers (PSPACE⊆ QIP⊆
EXP). Moreover they show that in the quantum case 3 communication
messages are enough (QIP= QIP(3)). They also show how to achieve per-
fect completeness and parallel ampliﬁcation for the model.
Department of Computer Science, Tel-Aviv University, Tel Aviv 69978, Israel. E-mail:
To whom correspondence should be addressed. E-mail: firstname.lastname@example.org
1570-0755/07/1200-0445/0 © 2007 Springer Science+Business Media, LLC