In this paper the evolution of some states of four qubits in [1] under global bipartite unitary operation and controlled by local unitary operation using four‐tangle [2] and the geometric invariants [3] is investigated. Particularly the entanglement distribution and properties of these four‐qubit states are studied.

AIP conference proceedingsJan 1, 20110 citations

Quantum Information Processing

Geometrical description of the dynamics of entangled two-qubit states under $U(2) \times U(2)$ local unitary operationsGeometrical description of the dynamics of entangled two-qubit states under $$U(2) \times U(2)$$ local unitary operations

Brahim Amghar, Mohammed Daoud A

Published Nov 17, 2021• 5 citations

Publisher

DOI: 10.1007/s11128-021-03341-4

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Geometrical description of the dynamics of entangled two-qubit states under

U(2) \times U(2)

local unitary operations

We refine recent local unitary entanglement classification for symmetric pure states of

n

qubits (that is, states invariant under permutations of qubits) using local unitary stabilizer subgroups and Majorana configurations. Stabilizer subgroups carry more entanglement distinguishing power than do the stabilizer subalgebras used in our previous work. We extend to mixed states recent results about local operations on pure symmetric states by showing that if two symmetric density operators are equivalent by a local unitary operation, then they are equivalent via a local unitary operation that is the {\em same} in each qubit. A geometric consequence, used in our entanglement classification, is that two symmetric pure states are local unitary equivalent if and only if their Majorana configurations can be interchanged by a rotation of the Bloch sphere.