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Geometric constructions over $\mathbb{C}$ and $\mathbb{F}_2$ for Quantum Information. (arXiv:1810.04258v1 [quant-ph])
来源于:arXiv
In this review paper I present two geometric constructions of distinguished
nature, one is over the field of complex numbers $\mathbb{C}$ and the other one
is over the two elements field $\mathbb{F}_2$. Both constructions have been
employed in the past fifteen years to describe two quantum paradoxes or two
resources of quantum information: entanglement of pure multipartite systems on
one side and contextuality on the other. Both geometric constructions are
linked to representation of semi-simple Lie groups/algebras. To emphasize this
aspect one explains on one hand how well-known results in representation theory
allows one to see all the classification of entanglement classes of various
tripartite quantum systems ($3$ qubits, $3$ fermions, $3$ bosonic qubits...) in
a unified picture. On the other hand, one also shows how some weight diagrams
of simple Lie groups are encapsulated in the geometry which deals with the
commutation relations of the generalized $N$-Pauli group. 查看全文>>