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

TL;DR

This paper derives closed-form upper bounds on three-way entanglement measures (three tangles) for three-qubit reduced states of four-qubit pure states, providing tighter constraints on entanglement distribution than previous bounds.

Contribution

It introduces new formulas for upper bounds on three tangles based on invariant polynomials, improving entanglement monogamy constraints for four-qubit states.

Findings

Derived closed-form upper bounds on three tangles.

Provided tighter entanglement constraints than previous work.

Enhanced understanding of three-qubit entanglement in four-qubit systems.

Abstract

Closed formulae for upper bound on three tangles of three-qubit reduced states in terms of three-qubit 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. [PRL 113, 110501 (2014), PRL 116, 049902(E) (2016)] to verify monogamy of four-qubit quantum entanglement.