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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Cited by in corpus (20)

• Coexistence of quantized and non-quantized geometric phases in quasi-one-dimensional systems without inversion symmetry
• Quantifying entanglement resources
• Geometric phases in quantum information
• Observation of Entanglement-Dependent Two-Particle Holonomic Phase
• Topological phase structure of vector vortex beams
• Topological phase structure of entangled qudits
• Fractional topological phase on spatially encoded photonic qudits
• Classification scheme of pure multipartite states based on topological phases
• Experimental observation of fractional topological phases with photonic qudits
• Three-qubit topological phase on entangled photon pairs
• Two-qudit topological phase evolution under dephasing
• Generalized W-state of four qubits with exclusively threetangle
• A Complete Set of Invariants for LU-Equivalence of Density Operators
• Complementarity between quantum entanglement, geometrical and dynamical appearances in N spin-$1/2$ system under all-range Ising model
• Non Abelian structures and the geometric phase of entangled qudits
• Maximal entanglement of two delocalized spin-$\frac{1}{2}$ particles
• Local unitary symmetries and entanglement invariants
• The Invariant Ring Of m Matrices Under The Adjoint Action By a Product Of General Linear Groups
• Intrinsic bounds of a two-qudit random evolution
• Witnessing entanglement via the geometric phase in a impurity-doped Bose-Einstein condensate