dorsal/arxiv
View SchemaQuantum and Classical Strong Direct Product Theorems and Optimal Time-Space Tradeoffs
| Authors | Hartmut Klauck, Robert Spalek, Ronald de Wolf |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0402123 |
| URL | https://arxiv.org/abs/quant-ph/0402123 |
Abstract
A 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.
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"abstract": "A strong direct product theorem says that if we want to compute k independent\ninstances of a function, using less than k times the resources needed for one\ninstance, then our overall success probability will be exponentially small in\nk. We establish such theorems for the classical as well as quantum query\ncomplexity of the OR function. This implies slightly weaker direct product\nresults for all total functions. We prove a similar result for quantum\ncommunication protocols computing k instances of the Disjointness function.\n Our direct product theorems imply a time-space tradeoff T^2*S=Omega(N^3) for\nsorting N items on a quantum computer, which is optimal up to polylog factors.\nThey also give several tight time-space and communication-space tradeoffs for\nthe problems of Boolean matrix-vector multiplication and matrix multiplication.",
"arxiv_id": "quant-ph/0402123",
"authors": [
"Hartmut Klauck",
"Robert Spalek",
"Ronald de Wolf"
],
"categories": [
"quant-ph",
"cs.CC"
],
"title": "Quantum and Classical Strong Direct Product Theorems and Optimal Time-Space Tradeoffs",
"url": "https://arxiv.org/abs/quant-ph/0402123"
},
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