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

Ciarán M. Lee, Matty J. Hoban

Research output: Contribution to journalArticlepeer-review

Abstract

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 QMAQMA is contained in PPPP, 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.
Original languageEnglish
Article number20160076
Number of pages19
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume472
Issue number2190
DOIs
Publication statusPublished - 1 Jun 2016

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