Built on

N. Bao, C. Cao, S. Fischetti and C. Keeler, Towards bulk metric reconstruction from extremal area variations , Class. Quant. Grav. 36
Original
1904
Earlier work this paper cites.
M. Bañados, C. Teitelboim and J. Zanelli, Black hole entropy and the dimensional continuation of the Gauss-Bonnet theorem , Phys. Rev. Lett. 72
1994
Earlier work this paper cites.
S. Carlip and C. Teitelboim, Aspects of black hole quantum mechanics and thermodynamics in 2+1 dimensions , Phys. Rev. D 51
1995
Earlier work this paper cites.
J. Maldacena, The large-N limit of superconformal field theories and supergravity , Int. J. Theor. Phys. 38
1999
Earlier work this paper cites.
C. A. Fuchs and J. van de Graaf, Cryptographic distinguishability measures for quantum mechanical states , IEEE Trans. Inf. Theory 45
1999
Earlier work this paper cites.
R. Bousso, Holography in general space-times , JHEP 1999
1999
Earlier work this paper cites.
G. Vidal, Entanglement monotones , J. Mod. Opt. 47
2000
Earlier work this paper cites.
B. M. Terhal, M. Horodecki, D. W. Leung and D. P. DiVincenzo, The entanglement of purification , J. Math. Phys 43
2002
Earlier work this paper cites.
P. Hayden and A. Winter, Communication cost of entanglement transformations , Phys. Rev. A 67
2003
Earlier work this paper cites.
S. Ryu and T. Takayanagi, Holographic derivation of entanglement entropy from the anti-de-Sitter space/conformal field theory correspondence , Phys. Rev. Lett. 96
2006
Earlier work this paper cites.
S. Ryu and T. Takayanagi, Aspects of holographic entanglement entropy , JHEP 08
2006
Earlier work this paper cites.
Y. Shi, L. Duan and G. Vidal, Classical simulation of quantum many-body systems with a tree tensor network , Phys. Rev. A 74
2006
Earlier work this paper cites.
A. Hamilton, D. Kabat, G. Lifschytz and D. A. Lowe, Holographic representation of local bulk operators , Phys. Rev. D 74
2006
Earlier work this paper cites.
V. E. Hubeny, M. Rangamani and T. Takayanagi, A covariant holographic entanglement entropy proposal , JHEP 07
Original
2007
Earlier work this paper cites.
G. Vidal, Entanglement renormalization , Phys. Rev. Lett. 99
2007
Earlier work this paper cites.
F. Verstraete, V. Murg and J. I. Cirac, Matrix product states, projected entangled pair states, and variational renormalization group methods for quantum spin systems , Adv. in Phys. 57
Original
2008
Earlier work this paper cites.
O. Aharony, O. Bergman, D. L. Jafferis and J. Maldacena, N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals , JHEP 2008
Original
2008
Earlier work this paper cites.
S. D. Mathur, The information paradox: a pedagogical introduction , Class. Quant. Grav. 26
Original
2009
Earlier work this paper cites.
M. Headrick, Entanglement Rényi entropies in holographic theories , Phys. Rev. D 82
Original
2010
Earlier work this paper cites.
B. Swingle, Entanglement renormalization and holography , Phys. Rev. D 86
Original
2012
Earlier work this paper cites.
P. Hayden and A. Winter, Weak decoupling duality and quantum identification , IEEE Trans. Inf. Theory 58
Original
2012
Earlier work this paper cites.
D. Marolf and A. C. Wall, Eternal black holes and superselection in AdS/CFT , Class. Quant. Grav. 30
Original
2012
Earlier work this paper cites.
B. Czech, J. L. Karczmarek, F. Nogueira and M. V. Raamsdonk, The gravity dual of a density matrix , Class. Quant. Grav 29
Original
2012
Earlier work this paper cites.

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2018

Beyond Toy Models: Distilling Tensor Networks in Full AdS/CFT

Bao, Ning, Penington, Geoffrey, Sorce, Jonathan et al.

Understand

We present a general procedure for constructing tensor networks that accurately reproduce holographic states in conformal field theories (CFTs).

Given a state in a large-$N$ CFT with a static, semiclassical gravitational dual, we build a tensor network by an iterative series of approximations that eliminate redundant degrees of freedom and minimize the bond dimensions of the resulting network.
We argue that the bond dimensions of the tensor network will match the areas of the corresponding bulk surfaces.
For 'tree' tensor networks (i.e., those that are constructed by discretizing spacetime with non-intersecting Ryu-Takayanagi surfaces), our arguments can be made rigorous using a version of one-shot entanglement distillation in the CFT.

Built on

N. Bao, C. Cao, S. Fischetti and C. Keeler, Towards bulk metric reconstruction from extremal area variations , Class. Quant. Grav. 36
Original
1904
Earlier work this paper cites.
M. Bañados, C. Teitelboim and J. Zanelli, Black hole entropy and the dimensional continuation of the Gauss-Bonnet theorem , Phys. Rev. Lett. 72
1994
Earlier work this paper cites.
S. Carlip and C. Teitelboim, Aspects of black hole quantum mechanics and thermodynamics in 2+1 dimensions , Phys. Rev. D 51
1995
Earlier work this paper cites.
J. Maldacena, The large-N limit of superconformal field theories and supergravity , Int. J. Theor. Phys. 38
1999
Earlier work this paper cites.
C. A. Fuchs and J. van de Graaf, Cryptographic distinguishability measures for quantum mechanical states , IEEE Trans. Inf. Theory 45
1999
Earlier work this paper cites.
R. Bousso, Holography in general space-times , JHEP 1999
1999
Earlier work this paper cites.
G. Vidal, Entanglement monotones , J. Mod. Opt. 47
2000
Earlier work this paper cites.
B. M. Terhal, M. Horodecki, D. W. Leung and D. P. DiVincenzo, The entanglement of purification , J. Math. Phys 43
2002
Earlier work this paper cites.
P. Hayden and A. Winter, Communication cost of entanglement transformations , Phys. Rev. A 67
2003
Earlier work this paper cites.
S. Ryu and T. Takayanagi, Holographic derivation of entanglement entropy from the anti-de-Sitter space/conformal field theory correspondence , Phys. Rev. Lett. 96
2006
Earlier work this paper cites.
S. Ryu and T. Takayanagi, Aspects of holographic entanglement entropy , JHEP 08
2006
Earlier work this paper cites.
Y. Shi, L. Duan and G. Vidal, Classical simulation of quantum many-body systems with a tree tensor network , Phys. Rev. A 74
2006
Earlier work this paper cites.
A. Hamilton, D. Kabat, G. Lifschytz and D. A. Lowe, Holographic representation of local bulk operators , Phys. Rev. D 74
2006
Earlier work this paper cites.
V. E. Hubeny, M. Rangamani and T. Takayanagi, A covariant holographic entanglement entropy proposal , JHEP 07
Original
2007
Earlier work this paper cites.
G. Vidal, Entanglement renormalization , Phys. Rev. Lett. 99
2007
Earlier work this paper cites.
F. Verstraete, V. Murg and J. I. Cirac, Matrix product states, projected entangled pair states, and variational renormalization group methods for quantum spin systems , Adv. in Phys. 57
Original
2008
Earlier work this paper cites.
O. Aharony, O. Bergman, D. L. Jafferis and J. Maldacena, N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals , JHEP 2008
Original
2008
Earlier work this paper cites.
S. D. Mathur, The information paradox: a pedagogical introduction , Class. Quant. Grav. 26
Original
2009
Earlier work this paper cites.
M. Headrick, Entanglement Rényi entropies in holographic theories , Phys. Rev. D 82
Original
2010
Earlier work this paper cites.
B. Swingle, Entanglement renormalization and holography , Phys. Rev. D 86
Original
2012
Earlier work this paper cites.
P. Hayden and A. Winter, Weak decoupling duality and quantum identification , IEEE Trans. Inf. Theory 58
Original
2012
Earlier work this paper cites.
D. Marolf and A. C. Wall, Eternal black holes and superselection in AdS/CFT , Class. Quant. Grav. 30
Original
2012
Earlier work this paper cites.
B. Czech, J. L. Karczmarek, F. Nogueira and M. V. Raamsdonk, The gravity dual of a density matrix , Class. Quant. Grav 29
Original
2012
Earlier work this paper cites.