The gravity dual of a density matrix
By B. Czech, Joanna L. Karczmarek, Fernando Nogueira, Mark Van Raamsdonk. 2012
499 citations recorded by the source corpus.
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.
Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/d9cd798d64669b256a4619aabdd2e742421ee901
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Citations in the corpus
- Lessons from the information paradox (2020, background): “It is generally believed in AdS/CFT that operators in any region on the boundary describe the bulk degrees of freedom in its entanglement wedge [140, 141].”
- Information radiation in BCFT models of black holes (2019, background): “Further insights in [1–3] make use of the notion of the “entanglement wedge” of a subsystem of a holographic system, which is the portion of the full spacetime that is dual to or reconstructable from the density matrix for the subsystem, and is understood to be the bulk region enclosed by the quantu”
- Wormholes, emergent gauge fields, and the weak gravity conjecture (2015, background): “It is worth emphasizing that if we should indeed understand the factorization as happening at this extremal surface, in order to reconstruct the Wilson line we still need to solve the problem of “entanglement wedge” reconstruction [67–69].”
- Bulk curves from boundary data in holography (2013, unknown): “discussed in [40, 41, 42, 43] (see also [44]).”
- Quantum extremal surfaces: holographic entanglement entropy beyond the classical regime (2014, background): “An important open question in AdS/CFT is how much of the bulk can be reconstructed from a specified boundary region R [23, 66, 67].”
- Replica wormholes and the black hole interior (2019, background): “The location of the entanglement wedge is significant because of the notion of “entanglement wedge reconstruction,”(18) which implies that in the large k phase, the radiation system R should (18)This was originally conjectured in [35, 36, 6], and established in [37, 38, 39] using the ideas of [8].”
- Comments on holographic complexity (2016, background): “We re-iterate that given the proposal that the mixed state associated with a subregion in the boundary theory is encoded in the corresponding entanglement wedge in the bulk [23, 24], it is natural that the holographic prescription for the complexity of this state should involve this bulk region.”
- A general proof of the quantum null energy condition (2017, background): “The entanglement wedge is believed to be the largest region containing information reconstructible using operators acting on the sub Hilbert space HA in the QFT [39–42], and so these bulk regions are causally constrained by the boundary theory.”
- Information flow in black hole evaporation (2019, background): “By entanglement wedge reconstruction [1, 25–30], this implies that after some time, QML plus the bath contain information about the interior of the black hole.”
- The Ryu–Takayanagi Formula from Quantum Error Correction (2016, background): “Moreover this reconstruction can be extended [12, 15–18] into the larger entanglement wedge of A, denoted EA and defined as the bulk domain of dependence of any bulk achronal surface Ξ whose only boundaries are A and the Hubeny/Rangamani/Takayanagi (HRT) surface γA associated to A [19].”
- Low-dimensional de Sitter quantum gravity (2019, background): “[87–97]), it should be fruitful to import these ideas to study the emergence of time in de Sitter.”
- Entanglement of purification through holographic duality (2017, background): “The bulk region dual to a reduced density matrix ρ AB is called the entanglement wedge [18–20] (more precisely the restriction of entanglement wedge on the canonical time slice), which we will write M AB .”
- Quantum extremal islands made easy. Part II. Black holes on the brane (2020, methodology): “Returning to the issue of extracting information from the island, entanglement wedge reconstruction [24, 131–137] allows us to recover information about the island with data from the boundary CFT in the corresponding boundary subregion.”
- Entanglement entropy from a holographic viewpoint (2012, background): “Indeed, the idea of holographic entanglement entropy has turned out to be closely related [193, 194] and more detailed analysis certainly deserves a future study.”
- The entropy of bulk quantum fields and the entanglement wedge of an evaporating black hole (2019, background): “A key concept in our current understanding of holographic dualities is the entanglement wedge WA of a bulk spacetime associated with a given region A in the dual holographic field theory [1–3].”
- Quantum extremal islands made easy. Part I. Entanglement on the brane (2020, methodology): “, see the lower panel in figure 8, we are able to recover information about the island with data from the boundary CFT in the corresponding boundary subregion, by applying standard entanglement wedge reconstruction [88–94].”
- Islands in cosmology (2020, methodology): “We assume the quantum focusing conjecture (QFC) [47] and entanglement wedge nesting (EWN) [18,19,105].”