Tight Product Monogamy Inequality for Entanglement

TL;DR

This paper establishes a precise monogamy inequality in product form for entanglement concurrence in tripartite quantum systems, enhancing understanding of entanglement sharing constraints.

Contribution

It proves a tight product-form monogamy relation for concurrence in pure tripartite states, extending previous sum-based inequalities.

Findings

The monogamy relation is saturated for canonical three-qubit states.

The relation applies to pure tripartite systems and is demonstrated with multiple examples.

Provides a new mathematical framework for understanding entanglement sharing constraints.

Abstract

Quantum entanglement for multiparty system has a unique feature when it comes to sharing its property among various subsystems. This is famously stated as the monogamy of entanglement. The traditional monogamy of concurrence for tripartite system was proved in a sum form. Recently, it was found that concurrence also respects a monogamy in the product form. Here, we prove a tight monogamy relation in the product form for the concurrence of pure tripartite systems. We illustrate our relation with several examples, including the canonical three qubit states, where this monogamy relation is saturated.