Generalized product-form monogamy relations in multi-qubit systems

TL;DR

This paper introduces generalized product-form monogamy inequalities for multi-qubit systems, providing tighter bounds on entanglement distribution using concurrence and negativity, applicable even to high-dimensional states.

Contribution

It presents new, tighter product-form monogamy inequalities for entanglement measures, extending their validity beyond previous limitations.

Findings

Product-form inequalities are tighter than existing ones.

New inequalities are valid for high-dimensional states.

Applicable to concurrence and negativity measures.

Abstract

Monogamy of entanglement essentially characterizes the entanglement distributions among the subsystems. Generally it is given by summation-form monogamy inequalities. In this paper, we present the product-form monogamy inequalities satisfied by the $\nu$-th ($\nu\geq2$) power of the concurrence. We show that they are tighter than the existing ones by detailed example. We then establish tighter product-form monogamy inequalities based on the negativity. We show that they are valid even for high dimensional states to which the well-known CKW inequality is violated.