Generalizations of the distributed Deutsch-Jozsa promise problem

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14330%2F17%3A00095802" target="_blank" >RIV/00216224:14330/17:00095802 - isvavai.cz</a>
Result on the web
<a href="http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=9690749&fileId=S0960129515000158" target="_blank" >http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=9690749&fileId=S0960129515000158</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1017/S0960129515000158" target="_blank" >10.1017/S0960129515000158</a>

Result language
angličtina
Original language name
Generalizations of the distributed Deutsch-Jozsa promise problem
Original language description
In the distributed Deutsch–Jozsa promise problem, two parties are to determine whether their respective strings x, y in {0,1} n are at the Hamming distance H(x, y) = 0 or H(x, y) = $frac{n}{2}$. Buhrman et al. (STOC' 98) proved that the exact quantum communication complexity of this problem is O(log n) while the deterministic communication complexity is Omega(n). This was the first impressive (exponential) gap between quantum and classical communication complexity. In this paper, we generalize the above distributed Deutsch-Jozsa promise problem to determine, for any fixed $frac{n}{2}$ <= k <= n, whether H(x, y) = 0 or H(x, y) = k, and show that an exponential gap between exact quantum and deterministic communication complexity still holds if k is an even such that $frac{1}{2}$n <= k < (1 - lambda)n, where 0 < lambda < $frac{1}{2}$ is given. We also deal with a promise version of the well-known disjointness problem and show also that for this promise problem there exists an exponential gap between quantum (and also probabilistic) communication complexity and deterministic communication complexity of the promise version of such a disjointness problem. Finally, some applications to quantum, probabilistic and deterministic finite automata of the results obtained are demonstrated.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Project
<a href="/en/project/EE2.3.30.0009" target="_blank" >EE2.3.30.0009: Employment of Newly Graduated Doctors of Science for Scientific Excellence</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2017
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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