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.
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