English

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 nn-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 4n2n14^n - 2n-1. An explicit transcendence basis is also exhibited.

Keywords

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