Upper bound on three-tangles of reduced states of four-qubit pure states

Abstract

Closed formulae for upper bound on three-tangles of three-qubit reduced states in terms of threequbit invariant polynomials of pure four-qubit states are obtained. Our results offer tighter constraints on total three-way entanglement of a given qubit with the rest of the system than those used in ref. [28,29] to verify monogamy of four-qubit quantum entanglement.