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

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

2005-03-04

arxiv.org/abs/quant-ph/0503052v2

J. Math. Phys. 46(10):102106, 2005

Physics

Quantum Physics

19 pages

Scientific paper

10.1063/1.2048327

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.

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