On parallel composition of zero-knowledge proofs with black-box quantum simulators

Authors:
Rahul Jain;Alexandra Kolla;Gatis Midrijanis;Ben W. Reichardt
Affiliations:
Centre for Quantum Technologies and Department of Computer Science, National University of Singapore, Singapore;EECS Department, Computer Science Division, University of California, Berkeley, Berkeley, California;EECS Department, Computer Science Division, University of California, Berkeley, Berkeley, California;School of Computer Science and Institute for Quantum Computing, University of Waterloo, Ontario, Canada
Venue:
Quantum Information & Computation
Year:
2009

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Abstract

Let L be a language decided by a constant-round quantum Arthur-Merlin (QAM) proto-col with negligible soundness error and all but possibly the last message being classical.We prove that if this protocol is zero knowledge with a black-box, quantum simulatorS, then L ∈ BQP. Our result also applies to any language having a three-round quan-tum interactive proof (QIP), with all but possibly the last message being classical, withnegligible soundness error and a black-box quantum simulator. These results in particular make it unlikely that certain protocols can be composed inparallel in order to reduce soundness error, while maintaining zero knowledge with ablack-box quantum simulator. They generalize analogous classical results of Goldreichand Krawczyk (1990). Our proof goes via a reduction to quantum black-box search. We show that the exis-tence of a black-box quantum simulator for such protocols when L ∉ BQP would implyan impossibly-good quantum search algorithm.