Topological phases and multiqubit entanglement

Details Topological phases and multiqubit entanglement Topological phases and multiqubit entanglement

2012-02-03

arxiv.org/abs/1202.0716v2

Phys. Rev. A 85, 032112 (2012)

Physics

Quantum Physics

Minor changes; journal reference added

Scientific paper

10.1103/PhysRevA.85.032112

Global phase factors of topological origin, resulting from cyclic local $\rm{SU}$ evolution, called topological phases, were first described in [Phys. Rev. Lett. {\bf 90}, 230403 (2003)], in the case of entangled qubit pairs. In this paper we investigate topological phases in multi-qubit systems as the result of cyclic local $\rm{SU(2)}$ evolution. These phases originate from the topological structure of the local $\rm{SU(2)}$-orbits and are an attribute of most entangled multi-qubit systems. We discuss the relation between topological phases and SLOCC-invariant polynomials and give examples where topological phases appear. A general method to find the values of the topological phases in an $n$-qubit system is described and a complete list of these phases for up to seven qubits is given.

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