The entropy cones of $W_N$ and $W_N^d$ states

TL;DR

This paper computes the quantum entropy cones for $W_N$ and $W_N^d$ states, revealing their structure and properties, including violations of monogamous mutual information for larger systems.

Contribution

It introduces the computation of quantum entropy cones for symmetric $W_N$ and $W_N^d$ states and models their structure using directed graph models.

Findings

Quantum entropy cones for $W_N$ and $W_N^d$ states are characterized.

Directed graph models effectively describe the symmetric quantum entropy cones.

Monogamous mutual information is violated for all $N>3$.

Abstract

The quantum entropy cones (QEC) for $W_N$ states of qubits and $W_N^d$ states of qudits are computed. These cones emerge as symmetrized quantum entropy cones (SQEC) for arbitrary $N$ and $d$. Directed graph models are presented which describe the SQEC for $W_N$ states and $W_N^d$ states. Monogamous mutual information (MMI) is violated for all $N>3$.