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On the rational invariants of quantum systems of $n$-qubits (2403.06346v2)
Published 11 Mar 2024 in math-ph, math.MP, math.QA, math.RA, math.RT, and quant-ph
Abstract: For an $n$-qubit system, a rational function on the space of mixed states which is invariant with respect to the action of the group of local symmetries may be viewed as a detailed measure of entanglement. We show that the field of all such invariant rational functions is purely transcendental over the complex numbers and has transcendence degree $4n - 2n-1$. An explicit transcendence basis is also exhibited.