A geometric formulation to measure global and genuine entanglement in three-qubit systems

Abstract We introduce a purely geometric formulation for two different measures addressed to quantify the entanglement between different parts of a tripartite qubit system. Our approach considers the entanglement–polytope defined by the smallest eigenvalues of the reduced density matrices of the qubit-components. The measures identify global and genuine entanglement, and are respectively associated with the projection and rejection of a given point of the polytope on the corresponding biseparable segments. Solving the so called ‘inverse problem’, we also discuss a way to force the system to behave in a particular form, which opens the possibility of controlling and manipulating entanglement for practical purposes.