Quantum Information: A Brief Overview and Some Mathematical Aspects

Maurice R. Kibler
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Maurice R. Kibler: CNRS/IN2P3, Institut de Physique Nucléaire, 69622 Villeurbanne, France

Mathematics, 2018, vol. 6, issue 12, 1-40

Abstract: 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.

Keywords: linearity; superposition; entanglement; mutually unbiased bases; SU(2); Galois fields; Galois rings (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2018
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