scholarly journals The complexity of the max word problem and the power of one-way interactive proof systems

1993 ◽  
Vol 3 (3) ◽  
pp. 292-305 ◽  
Author(s):  
Anne Condon
Keyword(s):  
Word Problem ◽  
Interactive Proof ◽  
Interactive Proof Systems ◽  
Proof Systems

Algebraic methods for interactive proof systems

1992 ◽  
Vol 39 (4) ◽  
pp. 859-868 ◽  
Author(s):  
Carsten Lund ◽  
Lance Fortnow ◽  
Howard Karloff ◽  
Noam Nisan
Keyword(s):  
Algebraic Methods ◽  
Interactive Proof ◽  
Interactive Proof Systems ◽  
Proof Systems

scholarly journals Bounds on the power of proofs and advice in general physical theories

2016 ◽  
Vol 472 (2190) ◽  
pp. 20160076 ◽  
Author(s):  
Ciarán M. Lee ◽  
Matty J. Hoban
Keyword(s):  
Quantum Theory ◽  
Quantum Structure ◽  
Interactive Proof ◽  
Interactive Proof Systems ◽  
Proof Systems ◽  
Local Measurements ◽  
General Physical ◽  
Adjoint Operators ◽  
Physical Features ◽  
Physical Principles

Quantum theory presents us with the tools for computational and communication advantages over classical theory. One approach to uncovering the source of these advantages is to determine how computation and communication power vary as quantum theory is replaced by other operationally defined theories from a broad framework of such theories. Such investigations may reveal some of the key physical features required for powerful computation and communication. In this paper, we investigate how simple physical principles bound the power of two different computational paradigms which combine computation and communication in a non-trivial fashion: computation with advice and interactive proof systems. We show that the existence of non-trivial dynamics in a theory implies a bound on the power of computation with advice. Moreover, we provide an explicit example of a theory with no non-trivial dynamics in which the power of computation with advice is unbounded. Finally, we show that the power of simple interactive proof systems in theories where local measurements suffice for tomography is non-trivially bounded. This result provides a proof that Q M A is contained in P P , which does not make use of any uniquely quantum structure—such as the fact that observables correspond to self-adjoint operators—and thus may be of independent interest.

scholarly journals On the complexity of approximating the diamond norm

2010 ◽  
Vol 10 (1&2) ◽  
pp. 77-86
Author(s):  
A. Ben-Aroya ◽  
A. Ta-Shma
Keyword(s):  
Convex Programming ◽  
Efficient Algorithm ◽  
Large Dimension ◽  
Interactive Proof ◽  
Interactive Proof Systems ◽  
Proof Systems ◽  
Operational Interpretation

The diamond norm is a norm defined over the space of quantum transformations. This norm has a natural operational interpretation: it measures how well one can distinguish between two transformations by applying them to a state of arbitrarily large dimension. This interpretation makes this norm useful in the study of quantum interactive proof systems. In this note we exhibit an efficient algorithm for computing this norm using convex programming. Independently of us, Watrous recently showed a different algorithm to compute this norm. An immediate corollary of this algorithm is a slight simplification of the argument of Kitaev and Watrous that QIP \subseteq \EXP.

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