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

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.

19 pages

References in corpus (9)

• Generalized Schmidt decomposition and classification of three-quantum-bit states
• Geometry of entangled states
• Computing Local Invariants of Qubit Systems
• Three-qubit pure-state canonical forms
• Non-local properties of multi-particle density matrices
• On local invariants of pure three-qubit states
• Local symmetry properties of pure 3-qubit states
• Measuring Polynomial Invariants of Multi-Party Quantum States
• Nonlocal Properties and Local Invariants for Bipartite Systems

Cited by in corpus (7)

• Topology of the three-qubit space of entanglement types
• Multiparty quantum states stabilized by the diagonal subgroup of the local unitary group
• Classification of nonproduct states with maximum stabilizer dimension
• Maximum stabilizer dimension for nonproduct states
• The stabilizer dimension of graph states
• Classification of n-qubit states with minimum orbit dimension
• Finite-Function-Encoding Quantum States