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Entanglement Wedge Reconstruction and Entanglement of Purification · Around

2018

Entanglement Wedge Reconstruction and Entanglement of Purification

Espíndola, Ricardo, Guijosa, Alberto, Pedraza, Juan F.

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In the holographic correspondence, subregion duality posits that knowledge of the mixed state of a finite spacelike region of the boundary theory allows full reconstruction of a specific region of the bulk, known as the entanglement wedge.

This statement has been proven for local bulk operators.
In this paper, specializing first for simplicity to a Rindler wedge of AdS$_3$, we find that generic curves within the wedge are in fact not fully reconstructible with entanglement entropies in the corresponding boundary region, even after using the most general variant of hole-ography, which was recently shown to suffice for reconstruction of arbitrary spacelike curves in the Poincare patch.
This limitation is an analog of the familiar phenomenon of entanglement shadows, which we call 'entanglement shade'.

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M. Bañados, C. Teitelboim and J. Zanelli, “The Black hole in three-dimensional space-time,” Phys. Rev. Lett. 69
1992
Earlier work this paper cites.
L. Susskind, L. Thorlacius and J. Uglum, “The Stretched horizon and black hole complementarity,” Phys. Rev. D 48
1993
Earlier work this paper cites.
S. S. Gubser, I. R. Klebanov and A. M. Polyakov, “Gauge theory correlators from non-critical string theory,” Phys. Lett. B 428
1998
Earlier work this paper cites.
E. Witten, “Anti-de Sitter space and holography,” Adv. Theor. Math. Phys. 2
1998
Earlier work this paper cites.
J. M. Maldacena, “The large N N limit of superconformal field theories and supergravity,” Adv. Theor. Math. Phys. 2
1999
Earlier work this paper cites.
I. Bena, “On the construction of local fields in the bulk of AdS(5) and other spaces,” Phys. Rev. D 62
2000
Earlier work this paper cites.
B. M. Terhal, M. Horodecki, D. W. Leung, D. P. DiVincenzo, “The entanglement of purification,” J. Math. Phys. 43
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.
A. Hamilton, D. N. Kabat, G. Lifschytz and D. A. Lowe, “Local bulk operators in AdS/CFT: A Boundary view of horizons and locality,” Phys. Rev. D 73
2007
Earlier work this paper cites.
M. M. Wolf, F. Verstraete, M. B. Hastings, J. I. Cirac, “Area laws in quantum systems: mutual information and correlations,” Phys. Rev. Lett. 100
Original
2008
Earlier work this paper cites.
E. Cáceres, M. Chernicoff, A. Güijosa and J. F. Pedraza, “Quantum Fluctuations and the Unruh Effect in Strongly-Coupled Conformal Field Theories,” JHEP 1006
Original
2010
Earlier work this paper cites.
M. Van Raamsdonk, “Comments on quantum gravity and entanglement,” arXiv:0907.2939 [hep-th]; “A patchwork description of dual spacetimes in AdS/CFT,” Class. Quant. Grav. 28
Original
2011
Earlier work this paper cites.
H. Casini and M. Huerta, “Entanglement entropy for the n n -sphere,” Phys. Lett. B 694
Original
2011
Earlier work this paper cites.
H. Casini, M. Huerta and R. C. Myers, “Towards a derivation of holographic entanglement entropy,” JHEP 1105
Original
2011
Earlier work this paper cites.
R. Bousso, S. Leichenauer and V. Rosenhaus, “Light-sheets and AdS/CFT,” Phys. Rev. D 86
Original
2012
Earlier work this paper cites.
V. E. Hubeny and M. Rangamani, “Causal Holographic Information,” JHEP 1206
Original
2012
Earlier work this paper cites.
B. Czech, J. L. Karczmarek, F. Nogueira and M. Van Raamsdonk, “The Gravity Dual of a Density Matrix,” Class. Quant. Grav. 29
Original
2012
Earlier work this paper cites.
I. Heemskerk, D. Marolf, J. Polchinski and J. Sully, “Bulk and Transhorizon Measurements in AdS/CFT,” JHEP 1210
Original
2012
Earlier work this paper cites.
B. Swingle, “Entanglement Renormalization and Holography,” Phys. Rev. D 86
Original
2012
Earlier work this paper cites.
A. Lewkowycz and J. Maldacena, “Generalized gravitational entropy,” JHEP 1308
Original
2013
Earlier work this paper cites.
T. Barrella, X. Dong, S. A. Hartnoll and V. L. Martin, “Holographic entanglement beyond classical gravity,” JHEP 1309
Original
2013
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.
R. Bousso, B. Freivogel, S. Leichenauer, V. Rosenhaus and C. Zukowski, “Null Geodesics, Local CFT Operators and AdS/CFT for Subregions,” Phys. Rev. D 88
Original
2013
Earlier work this paper cites.
V. E. Hubeny, H. Maxfield, M. Rangamani and E. Tonni, “Holographic entanglement plateaux,” JHEP 1308
Original
2013
Earlier work this paper cites.
X. Dong, “Holographic Entanglement Entropy for General Higher Derivative Gravity,” JHEP 1401
Original
2014
Earlier work this paper cites.
J. Camps, “Generalized entropy and higher derivative Gravity,” JHEP 1403
Original
2014
Earlier work this paper cites.

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