Quantum and Classical Strong Direct Product Theorems and Optimal Time-Space Tradeoffs

Simple item page
dc.creatorKlauck, Hartmut
dc.creatorSpalek, Robert
dc.creatorde Wolf, Ronald
dc.date2004-02-18
dc.date2004-07-30
dc.date.accessioned2026-07-07T06:09:01Z
dc.date.available2026-07-07T06:09:01Z
dc.descriptionA strong direct product theorem says that if we want to compute k independent instances of a function, using less than k times the resources needed for one instance, then our overall success probability will be exponentially small in k. We establish such theorems for the classical as well as quantum query complexity of the OR function. This implies slightly weaker direct product results for all total functions. We prove a similar result for quantum communication protocols computing k instances of the Disjointness function. Our direct product theorems imply a time-space tradeoff T^2*S=Omega(N^3) for sorting N items on a quantum computer, which is optimal up to polylog factors. They also give several tight time-space and communication-space tradeoffs for the problems of Boolean matrix-vector multiplication and matrix multiplication.
dc.description22 pages LaTeX. 2nd version: some parts rewritten, results are essentially the same. A shorter version will appear in IEEE FOCS 04
dc.identifierhttps://arxiv.org/abs/quant-ph/0402123
dc.identifierhttp://arxiv.org/abs/quant-ph/0402123
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/91834
dc.subjectQuantum Physics
dc.subjectComputational Complexity
dc.titleQuantum and Classical Strong Direct Product Theorems and Optimal Time-Space Tradeoffs
dc.typetext

Files

Collections

arXiv