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The Gravity Dual of a Density Matrix · Around

2012

The Gravity Dual of a Density Matrix

Czech, Bartlomiej, Karczmarek, Joanna L., Nogueira, Fernando et al.

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For a state in a quantum field theory on some spacetime, we can associate a density matrix to any subset of a given spacelike slice by tracing out the remaining degrees of freedom.

In the context of the AdS/CFT correspondence, if the original state has a dual bulk spacetime with a good classical description, it is natural to ask how much information about the bulk spacetime is carried by the density matrix for such a subset of field theory degrees of freedom.
In this note, we provide several constraints on the largest region that can be fully reconstructed, and discuss specific proposals for the geometric construction of this dual region.

Built on

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R. Bousso, S. Leichenauer and V. Rosenhaus, “Light-sheets and AdS/CFT,” arXiv:1203.6619 [hep-th]
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B. Swingle, “Entanglement Renormalization and Holography,” arXiv:0905.1317 [cond-mat.str-el]
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Then

S. Ryu and T. Takayanagi, “Holographic derivation of entanglement entropy from AdS/CFT,” Phys. Rev. Lett. 96
2006
Later among the works it cites.
V. E. Hubeny, M. Rangamani and T. Takayanagi, “A Covariant holographic entanglement entropy proposal,” JHEP 0707
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2007
Later among the works it cites.
M. Van Raamsdonk, “Building up spacetime with quantum entanglement,” Gen. Rel. Grav. 42
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2010
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M. Van Raamsdonk, “Comments on quantum gravity and entanglement,” arXiv:0907.2939 [hep-th]. M. Van Raamsdonk, “A patchwork description of dual spacetimes in AdS/CFT,” Class. Quant. Grav. 28
Original
2011
Later among the works it cites.

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