Open AccessFrom linear algebra to quantum information
Author(s) -
LW Yu,
NL Wang,
Shigeru Kanemitsu
Publication year - 2021
Publication title -
annals of mathematics and physics
Language(s) - English
Resource type - Journals
ISSN - 2689-7636
DOI - 10.17352/amp.000023
Subject(s) - operator algebra , algebra over a field , hilbert space , mathematics , sic povm , mathematical formulation of quantum mechanics , quantum mechanics , qubit , quantum information , quantum process , quantum probability , categorical quantum mechanics , quantum statistical mechanics , quantum operation , open quantum system , pure mathematics , physics , quantum , quantum dynamics
Anticipating the realization of quantum computers, we propose the most reader-friendly exposition of quantum information and qubits theory. Although the latter lies within framework of linear algebra, it has some fl avor of quantum mechanics and it would be easier to get used to special symbols and terminologies. Quantum mechanics is described in the language of functional analysis: the state space (the totality of all states) of a quantum system is a Hilbert space over the complex numbers and all mechanical quantities are taken as Hermite operators. Hence some basics of functional analysis is necessary. We make a smooth transition from linear algebra to functional analysis by comparing the elements in these theories: Hilbert space vs. fi nite dimensional vector space, Hermite operator vs. linear map given by a Hermite matrix. Then from Newtonian mechanics to quantum mechanics and then to the theory of qubits. We elucidate qubits theory a bit by accommodating it into linear algebra framework under these precursors.