Generalizations of the distributed Deutsch-Jozsa promise
problem

J 2017

Generalizations of the distributed Deutsch-Jozsa promise problem

GRUSKA, Jozef, Daowen QIU and Shenggen ZHENG

Basic information

Original name

Generalizations of the distributed Deutsch-Jozsa promise problem

Authors

GRUSKA, Jozef (703 Slovakia, belonging to the institution), Daowen QIU (156 China) and Shenggen ZHENG (156 China, guarantor, belonging to the institution)

Edition

Mathematical Structures in Computer Science, Cambridge University Press, 2017, 0960-1295

Other information

Language

English

Type of outcome

Článek v odborném periodiku

Field of Study

10201 Computer sciences, information science, bioinformatics

Country of publisher

United Kingdom of Great Britain and Northern Ireland

Confidentiality degree

není předmětem státního či obchodního tajemství

References:

URL

Impact factor

Impact factor: 1.094

RIV identification code

RIV/00216224:14330/17:00095802

Organization unit

Faculty of Informatics

DOI

http://dx.doi.org/10.1017/S0960129515000158

UT WoS

000395533500001

Keywords in English

Deutch Jozsa problem; quantum automata

Abstract

V originále

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.

Links

EE2.3.30.0009, research and development project

Name: Zaměstnáním čerstvých absolventů doktorského studia k vědecké excelenci

Citovat

GRUSKA, Jozef, Daowen QIU and Shenggen ZHENG. Generalizations of the distributed Deutsch-Jozsa promise problem. Mathematical Structures in Computer Science. Cambridge University Press, 2017, vol. 27, No 3, p. 311-331. ISSN 0960-1295. Available from: https://dx.doi.org/10.1017/S0960129515000158.

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   article_number = {3},
   doi = {http://dx.doi.org/10.1017/S0960129515000158},
   keywords = {Deutch Jozsa problem; quantum automata},
   language = {eng},
   issn = {0960-1295},
   journal = {Mathematical Structures in Computer Science},
   title = {Generalizations of the distributed Deutsch-Jozsa promise problem},
   url = {http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=9690749&fileId=S0960129515000158},
   volume = {27},
   year = {2017}
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KW  - Deutch Jozsa problem
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N2  - 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.
ER  -

GRUSKA, Jozef, Daowen QIU and Shenggen ZHENG. Generalizations of the distributed Deutsch-Jozsa promise problem. \textit{Mathematical Structures in Computer Science}. Cambridge University Press, 2017, vol.~27, No~3, p.~311-331. ISSN~0960-1295. Available from: https://dx.doi.org/10.1017/S0960129515000158.

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