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• W2022983207 abstract "The geometry of four-qubit entanglement is investigated. We replace some of the polynomial invariants for four-qubits introduced recently by new ones of direct geometrical meaning. It is shown that these invariants describe four points, six lines and four planes in complex projective space ${bf CP}^3$. For the generic entanglement class of stochastic local operations and classical communication they take a very simple form related to the elementary symmetric polynomials in four complex variables. Moreover, their magnitudes are entanglement monotones that fit nicely into the geometric set of $n$-qubit ones related to Grassmannians of $l$-planes found recently. We also show that in terms of these invariants the hyperdeterminant of order 24 in the four-qubit amplitudes takes a more instructive form than the previously published expressions available in the literature. Finally in order to understand two, three and four-qubit entanglement in geometric terms we propose a unified setting based on ${bf CP}^3$ furnished with a fixed quadric." @default.
• W2022983207 created "2016-06-24" @default.
• W2022983207 creator A5017479845 @default.
• W2022983207 date "2006-07-12" @default.
• W2022983207 modified "2023-09-26" @default.
• W2022983207 title "On the geometry of four-qubit invariants" @default.
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• W2022983207 doi "https://doi.org/10.1088/0305-4470/39/30/009" @default.
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