Generalized W-Class State and its Monogamy Relation

TL;DR

This paper extends the W class of quantum states from qubits to qudits and demonstrates that their entanglement properties are fully characterized by partial entanglements, even in mixed states involving a product state.

Contribution

It generalizes the W class states to higher-dimensional systems and establishes their entanglement characterization in mixed states.

Findings

Entanglement is fully characterized by partial entanglements.

Generalization from qubits to qudits.

Applicable to mixed states involving product states.

Abstract

We generalize the W class of states from $n$ qubits to $n$ qudits and prove that their entanglement is fully characterized by their partial entanglements even for the case of the mixture that consists of a W-class state and a product state $\ket{0}^{\otimes n}$.