Holographic Quantum Entanglement Negativity

TL;DR

This paper proposes a holographic conjecture for entanglement negativity in 2D conformal field theories, matching known results and linking negativity to holographic mutual information, with potential higher-dimensional extensions.

Contribution

It introduces a new holographic conjecture for entanglement negativity that reproduces replica results and relates negativity to holographic mutual information.

Findings

Conjecture matches replica technique results at large central charge.

Holographic negativity reduces to a sum of mutual informations.

Potential generalization to higher-dimensional AdS/CFT scenarios.

Abstract

We advance a holographic conjecture for the entanglement negativity of bipartite quantum states in $(1+1)$-dimensional conformal field theories in the $AdS_3/CFT_2$ framework. Our conjecture exactly reproduces the replica technique results in the large central charge limit, for both the pure state described by the $CFT_{1+1}$ vacuum dual to bulk the pure $AdS_3$ geometry and the finite temperature mixed state dual to a Euclidean BTZ black hole respectively. The holographic entanglement negativity characterizes the distillable entanglement and reduces to a specific sum of holographic mutual informations. We briefly allude to a possible higher dimensional generalization of our conjecture in a generic $AdS_{d+1}/CFT_{d}$ scenario.