Related papers: On the rational invariants of quantum systems of $n$-qubits

On the rational invariants of quantum systems of $n$-qubits

URL: http://arxiv.org/abs/2403.06346v2
Date: Tue, 12 Mar 2024 15:19:56 GMT
Title: On the rational invariants of quantum systems of $n$-qubits
Authors: Luca Candelori, Vladimir Y. Chernyak, and John R. Klein
Abstract summary: 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 $4n - 2n-1$.
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License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
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 $4^n - 2n-1$. An explicit transcendence basis is also exhibited.

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