On the variety of X-states

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发表日期：

2025年1月25日

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Luca Candelori,
Vladimir Y. Chernyak,
John R. Klein

摘要

We introduce the notion of an X-state on n-qubits. After taking the Zariski closure of the set of X-states in the space of all mixed states, we obtain a complex algebraic variety ${\mathscr {X}}$ $X$ that is equipped with the action of the Lie group of local symmetries G. We show that the field of G-invariant rational functions on ${\mathscr {X}}$ $X$ is purely transcendental over the complex numbers of degree $2^{2n-1}-n-1$ $2^{2 n - 1} - n - 1$ .