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Open AccessArticle

Quantum Information: A Brief Overview and Some Mathematical Aspects

1
CNRS/IN2P3, Institut de Physique Nucléaire, 69622 Villeurbanne, France
2
Faculté des Sciences et Technologies, Université Claude Bernard Lyon 1, 69622 Villeurbanne, France
3
Université de Lyon, 69361 Lyon, France
Mathematics 2018, 6(12), 273; https://doi.org/10.3390/math6120273
Received: 23 October 2018 / Revised: 14 November 2018 / Accepted: 20 November 2018 / Published: 22 November 2018
(This article belongs to the Special Issue Computer Algebra in Scientific Computing)
The aim of the present paper is twofold. First, to give the main ideas behind quantum computing and quantum information, a field based on quantum-mechanical phenomena. Therefore, a short review is devoted to (i) quantum bits or qubits (and more generally qudits), the analogues of the usual bits 0 and 1 of the classical information theory, and to (ii) two characteristics of quantum mechanics, namely, linearity, which manifests itself through the superposition of qubits and the action of unitary operators on qubits, and entanglement of certain multi-qubit states, a resource that is specific to quantum mechanics. A, second, focus is on some mathematical problems related to the so-called mutually unbiased bases used in quantum computing and quantum information processing. In this direction, the construction of mutually unbiased bases is presented via two distinct approaches: one based on the group SU(2) and the other on Galois fields and Galois rings. View Full-Text
Keywords: linearity; superposition; entanglement; mutually unbiased bases; SU(2); Galois fields; Galois rings linearity; superposition; entanglement; mutually unbiased bases; SU(2); Galois fields; Galois rings
MDPI and ACS Style

Kibler, M.R. Quantum Information: A Brief Overview and Some Mathematical Aspects. Mathematics 2018, 6, 273.

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