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arXiv · 1202.0716

Topological phases and multiqubit entanglement

Markus Johansson·Marie Ericsson·Kuldip Singh·Erik Sjöqvist·Mark S. Williamson
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Abstract

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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Markus Johansson, Marie Ericsson, Kuldip Singh, Erik Sjöqvist, Mark S. Williamson. 2012-03-14. Topological phases and multiqubit entanglement. https://doi.org/10.1103/physreva.85.032112

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