Effective reflected entropy and entanglement negativity for general 2D eternal black holes

Abstract

Both reflected entropy and entanglement negativity provide valid measures of entanglement between subsystems of a mixed state. For general 2D eternal black holes coupled with CFT matters in large c limit, we perform the replica-trick computation and find that both effective Renyi reflected entropy and effective entanglement negativity can be expressed in terms of the combination of modified backreacting cosmic branes in AdS 3 bulk. We then develop a holographic scheme to calculate effective reflected entropy and entanglement negativity for general 2D eternal black holes coupled with CFT matters in large c limit. Using the scheme, we check the consistency condition of the island formulae for entanglement negativity and reflected entropy. We find that the combinations of modified backreacting cosmic branes in AdS 3 bulk from the two island proposals of entanglement negativity exactly match with each other. Finally, we study the saturation of the reflected entropy inequality.

Entanglement negativity and defect extremal surface

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