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Then

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2016

Holographic Quantum Entanglement Negativity

Chaturvedi, Pankaj, Malvimat, Vinay, Sengupta, Gautam

Understand

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.

Built on

J. D. Brown and M. Henneaux, “Central charges in the canonical realization of asymptotic symmetries: an example from three-dimensional gravity,” Comm. Math. Phys
1986
Earlier work this paper cites.
A. B. Zamolodchikov and A. B. Zamolodchikov, “Structure constants and conformal bootstrap in Liouville field theory,” Nucl. Phys
1996
Earlier work this paper cites.
G. Vidal and R. F. Werner, “Computable measure of entanglement,” Phys. Rev. A
2002
Earlier work this paper cites.
P. Calabrese and J. L. Cardy, “Entanglement entropy and quantum field theory,” J. Stat. Mech
2004
Earlier work this paper cites.
M. B. Plenio, “Logarithmic Negativity: A Full Entanglement Monotone That is not Convex,” Phys. Rev. Lett
2005
Earlier work this paper cites.
S. Ryu and T. Takayanagi, “Holographic derivation of entanglement entropy from AdS/CFT,” Phys. Rev. Lett
2006
Earlier work this paper cites.
S. Ryu and T. Takayanagi, “Aspects of Holographic Entanglement Entropy,” JHEP
2006
Earlier work this paper cites.
T. Nishioka, S. Ryu, and T. Takayanagi, “Holographic Entanglement Entropy: An Overview,” J. Phys
Original
2009
Earlier work this paper cites.