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1 FEMTO-ST - Franche-Comté Électronique Mécanique, Thermique et Optique - Sciences et Technologies 2 Astronomical Institute of the Slovak Academy of Sciences

Abstract : Coding, transmission and recovery of quantum states with high security and efficiency, and with as low fluctuations as possible, is the main goal of quantum information protocols and their proper technical implementations. The paper deals with this topic, focusing on the quantum states related to Galois algebras. We first review the constructions of complete sets of mutually unbiased bases in a Hilbert space of dimension q = pm, with p being a prime and m a positive integer, employing the properties of Galois fields Fq for p > 2 and-or Galois rings of characteristic four R4m for p = 2. We then discuss the Gauss sums and their role in describing quantum phase fluctuations. Finally, we examine an intricate connection between the concepts of mutual unbiasedness and maximal entanglement.

Keywords : quantum information quantum phase algebraic methods finite fields finite rings

Author: Michel Planat - Metod Saniga -



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