English

Minimum orbit dimension for local unitary action on n-qubit pure states

Quantum Physics 2007-05-23 v2 Mathematical Physics math.MP

Abstract

The group of local unitary transformations partitions the space of n-qubit quantum states into orbits, each of which is a differentiable manifold of some dimension. We prove that all orbits of the n-qubit quantum state space have dimension greater than or equal to 3n/2 for n even and greater than or equal to (3n + 1)/2 for n odd. This lower bound on orbit dimension is sharp, since n-qubit states composed of products of singlets achieve these lowest orbit dimensions.

Keywords

Cite

@article{arxiv.quant-ph/0503052,
  title  = {Minimum orbit dimension for local unitary action on n-qubit pure states},
  author = {David W. Lyons and Scott N. Walck},
  journal= {arXiv preprint arXiv:quant-ph/0503052},
  year   = {2007}
}

Comments

19 pages

R2 v1 2026-07-22T19:48:09.766Z