The negativity contour: a quasi-local measure of entanglement for mixed states

Understand

In this paper, we study the entanglement structure of mixed states in quantum many-body systems using the $\textit{negativity contour}$, a local measure of entanglement that determines which real-space degrees of freedom in a subregion are contributing to the logarithmic negativity and with what magnitude.

• We construct an explicit contour function for Gaussian states using the fermionic partial-transpose.
• We generalize this contour function to generic many-body systems using a natural combination of derivatives of the logarithmic negativity.
• Though the latter negativity contour function is not strictly positive for all quantum systems, it is simple to compute and produces reasonable and interesting results.