Entanglement negativity and minimal entanglement wedge cross sections in holographic theories

TL;DR

This paper explores a holographic dual for logarithmic negativity, linking it to minimal entanglement wedge cross sections and quantum corrections, with tests in various AdS/CFT configurations.

Contribution

It proposes a new holographic dual for logarithmic negativity involving cosmic branes and quantum corrections, extending the understanding of entanglement measures in holography.

Findings

Logarithmic negativity equals the minimal cross section area of the entanglement wedge with quantum corrections.

The proposed dual accurately characterizes various subregion configurations in AdS${}_3$/CFT${}_2$.

The approach effectively describes the thermofield double state.

Abstract

We calculate logarithmic negativity, a quantum entanglement measure for mixed quantum states, in quantum error-correcting codes and find it to equal the minimal cross sectional area of the entanglement wedge in holographic codes with a quantum correction term equal to the logarithmic negativity between the bulk degrees of freedom on either side of the entanglement wedge cross section. This leads us to conjecture a holographic dual for logarithmic negativity that is related to the area of a cosmic brane with tension in the entanglement wedge plus a quantum correction term. This is closely related to (though distinct from) the holographic proposal for entanglement of purification. We check this relation for various configurations of subregions in AdS${}_3$/CFT${}_2$. These are disjoint intervals at zero temperature, as well as a single interval and adjacent intervals at finite temperature. We also find this prescription to effectively characterize the thermofield double state. We discuss how a deformation of a spherical entangling region complicates calculations and speculate how to generalize to a covariant description.