Operational Entanglement Families of Symmetric Mixed N-Qubit States

TL;DR

This paper introduces a practical classification scheme for entanglement in symmetric mixed states of multiple qubits, enabling experimental realization and distinction of different entanglement families using witness operators.

Contribution

It presents an operational classification of symmetric mixed states based on SLOCC, proves their measure, and links theoretical families to experimental parameters.

Findings

Defined entanglement families with non-zero measure

Constructed witness operators to distinguish families

Established a correspondence for laboratory realization

Abstract

We introduce an operational entanglement classification of symmetric mixed states for an arbitrary number of qubits based on stochastic local operations assisted with classical communication (SLOCC operations). We define families of SLOCC entanglement classes successively embedded into each other, we prove that they are of non-zero measure, and we construct witness operators to distinguish them. Moreover, we discuss how arbitrary symmetric mixed states can be realized in the lab via a one-to-one correspondence between well-defined sets of controllable parameters and the corresponding entanglement families.