Built on

J. Kirklin, “Unambiguous Phase Spaces for Subregions,” arXiv:1901.09857 [hep-th]
Original
1901
Earlier work this paper cites.
M. V. Berry, “Quantal phase factors accompanying adiabatic changes,” Proc. Roy. Soc. Lond. A 392
1984
Earlier work this paper cites.
F. Wilczek and A. Zee, “Appearance of Gauge Structure in Simple Dynamical Systems,” Phys. Rev. Lett. 52
1984
Earlier work this paper cites.
V. Coffman, J. Kundu and W. K. Wootters, “Distributed entanglement,” Phys. Rev. A 61
2000
Earlier work this paper cites.
W. Dür, G. Vidal and J. I. Cirac, “Three qubits can be entangled in two inequivalent ways,” Phys. Rev. A 62
2000
Earlier work this paper cites.
F. Verstraete, J. Dehaene, B. de Moor and H. Verschelde, “Four qubits can be entangled in nine different ways,” Phys. Rev. A 65, 052112 (2002) [quant-ph/0109033]
2002
Earlier work this paper cites.
S. Ryu and T. Takayanagi, “Holographic derivation of entanglement entropy from AdS/CFT,” Phys. Rev. Lett. 96
2006
Earlier work this paper cites.
V. E. Hubeny, M. Rangamani and T. Takayanagi, “A Covariant holographic entanglement entropy proposal,” JHEP 0707
Original
2007
Earlier work this paper cites.
M. Van Raamsdonk, “Building up spacetime with quantum entanglement,” Gen. Rel. Grav. 42
Original
2010
Earlier work this paper cites.
T. Faulkner, A. Lewkowycz and J. Maldacena, “Quantum corrections to holographic entanglement entropy,” JHEP 1311
Original
2013
Earlier work this paper cites.
J. Maldacena and L. Susskind, “Cool horizons for entangled black holes,” Fortsch. Phys. 61
Original
2013
Earlier work this paper cites.
K. Papadodimas and S. Raju, “State-Dependent Bulk-Boundary Maps and Black Hole Complementarity,” Phys. Rev. D 89
Original
2014
Earlier work this paper cites.

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2019

A Modular Sewing Kit for Entanglement Wedges

Czech, Bartlomiej, de Boer, Jan, Ge, Dongsheng et al.

Understand

We relate the Riemann curvature of a holographic spacetime to an entanglement property of the dual CFT state: the Berry curvature of its modular Hamiltonians.

The modular Berry connection encodes the relative bases of nearby CFT subregions while its bulk dual, restricted to the code subspace, relates the edge-mode frames of the corresponding entanglement wedges.
At leading order in 1/N and for sufficiently smooth HRRT surfaces, the modular Berry connection simply sews together the orthonormal coordinate systems covering neighborhoods of HRRT surfaces.
This geometric perspective on entanglement is a promising new tool for connecting the dynamics of entanglement and gravitation.

Built on

J. Kirklin, “Unambiguous Phase Spaces for Subregions,” arXiv:1901.09857 [hep-th]
Original
1901
Earlier work this paper cites.
M. V. Berry, “Quantal phase factors accompanying adiabatic changes,” Proc. Roy. Soc. Lond. A 392
1984
Earlier work this paper cites.
F. Wilczek and A. Zee, “Appearance of Gauge Structure in Simple Dynamical Systems,” Phys. Rev. Lett. 52
1984
Earlier work this paper cites.
V. Coffman, J. Kundu and W. K. Wootters, “Distributed entanglement,” Phys. Rev. A 61
2000
Earlier work this paper cites.
W. Dür, G. Vidal and J. I. Cirac, “Three qubits can be entangled in two inequivalent ways,” Phys. Rev. A 62
2000
Earlier work this paper cites.
F. Verstraete, J. Dehaene, B. de Moor and H. Verschelde, “Four qubits can be entangled in nine different ways,” Phys. Rev. A 65, 052112 (2002) [quant-ph/0109033]
2002
Earlier work this paper cites.
S. Ryu and T. Takayanagi, “Holographic derivation of entanglement entropy from AdS/CFT,” Phys. Rev. Lett. 96
2006
Earlier work this paper cites.
V. E. Hubeny, M. Rangamani and T. Takayanagi, “A Covariant holographic entanglement entropy proposal,” JHEP 0707
Original
2007
Earlier work this paper cites.
M. Van Raamsdonk, “Building up spacetime with quantum entanglement,” Gen. Rel. Grav. 42
Original
2010
Earlier work this paper cites.
T. Faulkner, A. Lewkowycz and J. Maldacena, “Quantum corrections to holographic entanglement entropy,” JHEP 1311
Original
2013
Earlier work this paper cites.
J. Maldacena and L. Susskind, “Cool horizons for entangled black holes,” Fortsch. Phys. 61
Original
2013
Earlier work this paper cites.
K. Papadodimas and S. Raju, “State-Dependent Bulk-Boundary Maps and Black Hole Complementarity,” Phys. Rev. D 89
Original
2014
Earlier work this paper cites.