Non-Gaussianity in mixed states via replica twist entropy

Determine whether the replica twist entropy or suitable generalizations can extract useful information about non-Gaussianity in mixed quantum states.

Background

The paper introduces the replica twist entropy as a two-copy diagnostic of fermionic non-Gaussianity for pure states and analyzes its general properties, including its behavior in Haar-random states and in thermofield-double states of the Sachdev–Ye–Kitaev model. The construction and results in the paper are restricted to pure states.

The authors explicitly identify the extension to mixed states as unresolved, asking whether the replica twist entropy or generalizations of it can provide useful information about mixed-state non-Gaussianity. This is presented as a direction for future work rather than a problem resolved by the paper.