Generalizations of the distributed Deutsch-Jozsa promise problem

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.

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

• Original language: English
• Type of outcome: Article in a journal
• Field of Study: 10201 Computer sciences, information science, bioinformatics
• Country of publisher: United Kingdom of Great Britain and Northern Ireland
• Confidentiality degree: is not subject to a state or trade secret
• WWW: 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
• Tags: International impact, Reviewed

Abstract

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