Topological phases and multiqubit entanglement

Abstract

Global phase factors of topological origin, resulting from cyclic local $\mathrm{SU}$ 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 $\mathrm{SU}(2)$ evolution. These phases originate from the topological structure of the local $\mathrm{SU}(2)$-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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References in corpus (5)

• Constructing N-qubit entanglement monotones from anti-linear operators
• Entanglement monotones and maximally entangled states in multipartite qubit systems
• On polynomial invariants of several qubits
• Phase Dynamics of Two Entangled Qubits
• Experimental Observation of a Topological Phase in the Maximally Entangled State of a Pair of Qubits