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International Journal of Theoretical Physics

, Volume 58, Issue 1, pp 247–254 | Cite as

Quantum Communication Based on an Algorithm of Determining a Matrix

  • Koji NagataEmail author
  • Tadao Nakamura
Article
  • 34 Downloads

Abstract

Let us consider the following game; Bob has a N × M matrix (N rows and M columns) but Alice does not know what matrix he has. The goal is of knowing the unknown matrix. How many queries does she need? In the classical case, she needs N × M queries. In the quantum case, she needs just a query. We propose an algorithm for determining the N × M matrix (N rows and M columns). First, we discuss an algorithm for determining an integer string. The algorithm presented here has the following structure. Given the set of real values {a1, a2, a3,…, aN} and a special function g, we determine N values of the function g(a1), g(a2), g(a3),…, g(aN) simultaneously. The speed of determining the string is shown to outperform the best classical case by a factor of N. Next, we consider it as a column of the matrix; C1 = (g(a1), g(a2), g(a3),…, g(aN)) = (a11, a21,..., an1). By using M parallel quantum systems, we have M columns simultaneously, C1, C2,..., CM. The speed of obtaining the M columns (the matrix) is shown to outperform the classical case by a factor of N × M. This implies she needs just a query.

Keywords

Quantum algorithms Quantum communication Quantum computation 

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of PhysicsKorea Advanced Institute of Science and TechnologyDaejeonKorea
  2. 2.Department of Information and Computer ScienceKeio UniversityYokohamaJapan

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