Vanishing of n=2 genuine multi-entropy for fermionic Gaussian states

Determine whether the genuine Rényi tri-partite multi-entropy GM⁽³⁾₂ vanishes for tripartite fermionic Gaussian states.

Background

The paper proves that GM⁽³⁾₂ vanishes for every pure bosonic Gaussian state, including states with position-momentum correlations. The proof relies on a factorization property of the n=2, three-party replica partition function.

The authors propose extending the analysis to fermionic Gaussian states, which, like bosonic Gaussian states, can be characterized through Kähler structures. Comparing the fermionic result with conformal-field-theory predictions is identified as a related motivation.