On the rational invariants of quantum systems of $n$-qubits
Mathematical Physics
2024-03-13 v2 math.MP
Quantum Algebra
Rings and Algebras
Representation Theory
Quantum Physics
Abstract
For an -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 . An explicit transcendence basis is also exhibited.
Cite
@article{arxiv.2403.06346,
title = {On the rational invariants of quantum systems of $n$-qubits},
author = {Luca Candelori and Vladimir Y. Chernyak and John R. Klein},
journal= {arXiv preprint arXiv:2403.06346},
year = {2024}
}
Comments
greatly simplified the treatment of quotients