Space from Hilbert space: Recovering geometry from bulk entanglement

Cao, ChunJun; Carroll, Sean M.; Michalakis, Spyridon

doi:10.1103/physrevd.95.024031

Title: Space from Hilbert space: Recovering geometry from bulk entanglement

Journal Article · Sun Jan 01 00:00:00 EST 2017 · Physical Review D

DOI:https://doi.org/10.1103/physrevd.95.024031· OSTI ID:1536213

Cao, ChunJun; Carroll, Sean M.; Michalakis, Spyridon

Not provided.

Cite

Export

Save

Research Organization:: California Institute of Technology (CalTech), Pasadena, CA (United States)

Sponsoring Organization:: USDOE Office of Science (SC)

DOE Contract Number:: SC0011632

OSTI ID:: 1536213

Journal Information:: Physical Review D, Vol. 95, Issue 2; ISSN 2470-0010

Publisher:: American Physical Society (APS)

Country of Publication:: United States

Language:: English

References (82)

Quantum sine-Gordon equation as the massive Thirring model Coleman, Sidney Physical Review D, Vol. 11, Issue 8 https://doi.org/10.1103/PhysRevD.11.2088	journal	April 1975
The Large-N Limit of Superconformal Field Theories and Supergravity Maldacena, Juan International Journal of Theoretical Physics, Vol. 38, Issue 4, p. 1113-1133 https://doi.org/10.1023/A:1026654312961	journal	January 1999
The large $N$ limit of superconformal field theories and supergravity Maldacena, Juan Advances in Theoretical and Mathematical Physics, Vol. 2, Issue 2 https://doi.org/10.4310/ATMP.1998.v2.n2.a1	journal	January 1998
Relative entropy and holography Blanco, David D.; Casini, Horacio; Hung, Ling-Yan Journal of High Energy Physics, Vol. 2013, Issue 8 https://doi.org/10.1007/JHEP08(2013)060	journal	August 2013
Gravitation from entanglement in holographic CFTs Faulkner, Thomas; Guica, Monica; Hartman, Thomas Journal of High Energy Physics, Vol. 2014, Issue 3 https://doi.org/10.1007/JHEP03(2014)051	journal	March 2014
Locality of Gravitational Systems from Entanglement of Conformal Field Theories Lin, Jennifer; Marcolli, Matilde; Ooguri, Hirosi Physical Review Letters, Vol. 114, Issue 22 https://doi.org/10.1103/PhysRevLett.114.221601	journal	June 2015
Tensor Network States and Geometry Evenbly, G.; Vidal, G. Journal of Statistical Physics, Vol. 145, Issue 4 https://doi.org/10.1007/s10955-011-0237-4	journal	June 2011
Entanglement renormalization and holography Swingle, Brian Physical Review D, Vol. 86, Issue 6 https://doi.org/10.1103/PhysRevD.86.065007	journal	September 2012
Consistency conditions for an AdS multiscale entanglement renormalization ansatz correspondence Bao, Ning; Cao, ChunJun; Carroll, Sean M. Physical Review D, Vol. 91, Issue 12 https://doi.org/10.1103/PhysRevD.91.125036	journal	June 2015
Tensor network quotient takes the vacuum to the thermal state Czech, Bartłomiej; Evenbly, Glen; Lamprou, Lampros Physical Review B, Vol. 94, Issue 8 https://doi.org/10.1103/PhysRevB.94.085101	journal	August 2016
Tensor networks from kinematic space Czech, Bartlomiej; Lamprou, Lampros; McCandlish, Samuel Journal of High Energy Physics, Vol. 2016, Issue 7 https://doi.org/10.1007/JHEP07(2016)100	journal	July 2016
Holographic quantum error-correcting codes: toy models for the bulk/boundary correspondence Pastawski, Fernando; Yoshida, Beni; Harlow, Daniel Journal of High Energy Physics, Vol. 2015, Issue 6 https://doi.org/10.1007/JHEP06(2015)149	journal	June 2015
Holographic duality from random tensor networks Hayden, Patrick; Nezami, Sepehr; Qi, Xiao-Liang Journal of High Energy Physics, Vol. 2016, Issue 11 https://doi.org/10.1007/JHEP11(2016)009	journal	November 2016
Cool horizons for entangled black holes Maldacena, J.; Susskind, L. Fortschritte der Physik, Vol. 61, Issue 9 https://doi.org/10.1002/prop.201300020	journal	August 2013
Building up spacetime with quantum entanglement Van Raamsdonk, Mark General Relativity and Gravitation, Vol. 42, Issue 10 https://doi.org/10.1007/s10714-010-1034-0	journal	June 2010
Holographic Dual of an Einstein-Podolsky-Rosen Pair has a Wormhole Jensen, Kristan; Karch, Andreas Physical Review Letters, Vol. 111, Issue 21 https://doi.org/10.1103/PhysRevLett.111.211602	journal	November 2013
Splitting spacetime and cloning qubits: linking no-go theorems across the ER=EPR duality: Splitting spacetime and cloning qubits Bao, Ning; Pollack, Jason; Remmen, Grant N. Fortschritte der Physik, Vol. 63, Issue 11-12 https://doi.org/10.1002/prop.201500053	journal	November 2015
Wormhole and entanglement (non-)detection in the ER=EPR correspondence Bao, Ning; Pollack, Jason; Remmen, Grant N. Journal of High Energy Physics, Vol. 2015, Issue 11 https://doi.org/10.1007/JHEP11(2015)126	journal	November 2015
Entanglement conservation, ER=EPR, and a new classical area theorem for wormholes Remmen, Grant N.; Bao, Ning; Pollack, Jason Journal of High Energy Physics, Vol. 2016, Issue 7 https://doi.org/10.1007/JHEP07(2016)048	journal	July 2016
On the weight of entanglement Bruschi, David Edward Physics Letters B, Vol. 754 https://doi.org/10.1016/j.physletb.2016.01.034	journal	March 2016
Entanglement Equilibrium and the Einstein Equation Jacobson, Ted Physical Review Letters, Vol. 116, Issue 20 https://doi.org/10.1103/PhysRevLett.116.201101	journal	May 2016
Comments on Jacobson’s “entanglement equilibrium and the Einstein equation” Casini, Horacio; Galante, Damián A.; Myers, Robert C. Journal of High Energy Physics, Vol. 2016, Issue 3 https://doi.org/10.1007/JHEP03(2016)194	journal	March 2016
What is the entropy in entropic gravity? Carroll, Sean M.; Remmen, Grant N. Physical Review D, Vol. 93, Issue 12 https://doi.org/10.1103/PhysRevD.93.124052	journal	June 2016
Universal upper bound on the entropy-to-energy ratio for bounded systems Bekenstein, Jacob D. Physical Review D, Vol. 23, Issue 2 https://doi.org/10.1103/PhysRevD.23.287	journal	January 1981
Entropy bounds and black hole remnants Bekenstein, Jacob D. Physical Review D, Vol. 49, Issue 4 https://doi.org/10.1103/PhysRevD.49.1912	journal	February 1994
A covariant entropy conjecture Bousso, Raphael Journal of High Energy Physics, Vol. 1999, Issue 07 https://doi.org/10.1088/1126-6708/1999/07/004	journal	July 1999
The world as a hologram Susskind, Leonard Journal of Mathematical Physics, Vol. 36, Issue 11 https://doi.org/10.1063/1.531249	journal	November 1995
Colloquium : Area laws for the entanglement entropy Eisert, J.; Cramer, M.; Plenio, M. B. Reviews of Modern Physics, Vol. 82, Issue 1 https://doi.org/10.1103/RevModPhys.82.277	journal	February 2010
Quantum source of entropy for black holes Bombelli, Luca; Koul, Rabinder K.; Lee, Joohan Physical Review D, Vol. 34, Issue 2 https://doi.org/10.1103/PhysRevD.34.373	journal	July 1986
Entropy and area Srednicki, Mark Physical Review Letters, Vol. 71, Issue 5 https://doi.org/10.1103/PhysRevLett.71.666	journal	August 1993
Area Laws in Quantum Systems: Mutual Information and Correlations Wolf, Michael M.; Verstraete, Frank; Hastings, Matthew B. Physical Review Letters, Vol. 100, Issue 7 https://doi.org/10.1103/PhysRevLett.100.070502	journal	February 2008
Holographic Derivation of Entanglement Entropy from the anti–de Sitter Space/Conformal Field Theory Correspondence Ryu, Shinsei; Takayanagi, Tadashi Physical Review Letters, Vol. 96, Issue 18 https://doi.org/10.1103/PhysRevLett.96.181602	journal	May 2006
A covariant holographic entanglement entropy proposal Hubeny, Veronika E.; Rangamani, Mukund; Takayanagi, Tadashi Journal of High Energy Physics, Vol. 2007, Issue 07 https://doi.org/10.1088/1126-6708/2007/07/062	journal	July 2007
Quantum corrections to holographic entanglement entropy Faulkner, Thomas; Lewkowycz, Aitor; Maldacena, Juan Journal of High Energy Physics, Vol. 2013, Issue 11 https://doi.org/10.1007/JHEP11(2013)074	journal	November 2013
Quantum Bousso bound Strominger, Andrew; Thompson, David Physical Review D, Vol. 70, Issue 4 https://doi.org/10.1103/PhysRevD.70.044007	journal	August 2004
Proof of a quantum Bousso bound Bousso, Raphael; Casini, Horacio; Fisher, Zachary Physical Review D, Vol. 90, Issue 4 https://doi.org/10.1103/PhysRevD.90.044002	journal	August 2014
Entropy on a null surface for interacting quantum field theories and the Bousso bound Bousso, Raphael; Casini, Horacio; Fisher, Zachary Physical Review D, Vol. 91, Issue 8 https://doi.org/10.1103/PhysRevD.91.084030	journal	April 2015
Relative entropy and the Bekenstein bound Casini, H. Classical and Quantum Gravity, Vol. 25, Issue 20 https://doi.org/10.1088/0264-9381/25/20/205021	journal	September 2008
On the architecture of spacetime geometry Bianchi, Eugenio; Myers, Robert C. Classical and Quantum Gravity, Vol. 31, Issue 21 https://doi.org/10.1088/0264-9381/31/21/214002	journal	October 2014
Renormalization of entanglement entropy and the gravitational effective action Cooperman, Joshua H.; Luty, Markus A. Journal of High Energy Physics, Vol. 2014, Issue 12 https://doi.org/10.1007/JHEP12(2014)045	journal	December 2014
On spacetime entanglement Myers, Robert C.; Pourhasan, Razieh; Smolkin, Michael Journal of High Energy Physics, Vol. 2013, Issue 6 https://doi.org/10.1007/JHEP06(2013)013	journal	June 2013
Gravitation and Vacuum Entanglement Entropy Jacobson, Ted International Journal of Modern Physics D, Vol. 21, Issue 11 https://doi.org/10.1142/S0218271812420060	journal	October 2012
Holographic entropy inequalities and gapped phases of matter Bao, Ning; Cao, ChunJun; Walter, Michael Journal of High Energy Physics, Vol. 2015, Issue 9 https://doi.org/10.1007/JHEP09(2015)203	journal	September 2015
The holographic entropy cone Bao, Ning; Nezami, Sepehr; Ooguri, Hirosi Journal of High Energy Physics, Vol. 2015, Issue 9 https://doi.org/10.1007/JHEP09(2015)130	journal	September 2015
Spectral Gap and Exponential Decay of Correlations Hastings, Matthew B.; Koma, Tohru Communications in Mathematical Physics, Vol. 265, Issue 3 https://doi.org/10.1007/s00220-006-0030-4	journal	April 2006
Embedding metric spaces in Euclidean space Morgan, C. L. Journal of Geometry, Vol. 5, Issue 1 https://doi.org/10.1007/BF01954540	journal	March 1974
Generalized multidimensional scaling: A framework for isometry-invariant partial surface matching Bronstein, A. M.; Bronstein, M. M.; Kimmel, R. Proceedings of the National Academy of Sciences, Vol. 103, Issue 5 https://doi.org/10.1073/pnas.0508601103	journal	January 2006
Equal-time correlations in Haldane-gap antiferromagnets So/rensen, Erik S.; Affleck, Ian Physical Review B, Vol. 49, Issue 22 https://doi.org/10.1103/PhysRevB.49.15771	journal	June 1994
Monte-Carlo study of correlations in quantum spin chains at non-zero temperature Kim, Y. J.; Greven, M.; Wiese, U. -J. The European Physical Journal B, Vol. 4, Issue 3 https://doi.org/10.1007/s100510050382	journal	August 1998
Fault-tolerant quantum computation by anyons Kitaev, A. Yu. Annals of Physics, Vol. 303, Issue 1 https://doi.org/10.1016/S0003-4916(02)00018-0	journal	January 2003
Bipartite entanglement and entropic boundary law in lattice spin systems Hamma, Alioscia; Ionicioiu, Radu; Zanardi, Paolo Physical Review A, Vol. 71, Issue 2 https://doi.org/10.1103/PhysRevA.71.022315	journal	February 2005
Class of Quantum Many-Body States That Can Be Efficiently Simulated Vidal, G. Physical Review Letters, Vol. 101, Issue 11 https://doi.org/10.1103/PhysRevLett.101.110501	journal	September 2008
On the modular structure of local algebras of observables Fredenhagen, Klaus Communications in Mathematical Physics, Vol. 97, Issue 1-2 https://doi.org/10.1007/BF01206179	journal	March 1985
Lorentz Invariance and Quantum Gravity: An Additional Fine-Tuning Problem? Collins, John; Perez, Alejandro; Sudarsky, Daniel Physical Review Letters, Vol. 93, Issue 19 https://doi.org/10.1103/PhysRevLett.93.191301	journal	November 2004
Von Neumann algebra automorphisms and time-thermodynamics relation in generally covariant quantum theories Connes, A.; Rovelli, C. Classical and Quantum Gravity, Vol. 11, Issue 12 https://doi.org/10.1088/0264-9381/11/12/007	journal	December 1994
General relativity without coordinates Regge, T. Il Nuovo Cimento, Vol. 19, Issue 3 https://doi.org/10.1007/BF02733251	journal	February 1961
On the Modular Structure of Local Algebras of Observables Fredenhagen, Klaus Quantum Field Theory https://doi.org/10.1007/978-3-642-70307-2_5	book	January 1985
Entropy bounds and black hole remnants Bekenstein, Jacob D. Jacob Bekenstein https://doi.org/10.1142/9789811203961_0028	book	September 2019
The large N limit of superconformal field theories and supergravity Maldacena, Juan The second meeting on trends in theoretical physics, AIP Conference Proceedings https://doi.org/10.1063/1.59653	conference	January 1999
A Covariant Holographic Entanglement Entropy Proposal Hubeny, Veronika E.; Rangamani, Mukund; Takayanagi, Tadashi arXiv https://doi.org/10.48550/arxiv.0705.0016	text	January 2007
Relative entropy and the Bekenstein bound Casini, H. arXiv https://doi.org/10.48550/arxiv.0804.2182	text	January 2008
Tensor network states and geometry Evenbly, G.; Vidal, G. arXiv https://doi.org/10.48550/arxiv.1106.1082	text	January 2011
Gravitation and vacuum entanglement entropy Jacobson, Ted arXiv https://doi.org/10.48550/arxiv.1204.6349	text	January 2012
On the Architecture of Spacetime Geometry Bianchi, Eugenio; Myers, Robert C. arXiv https://doi.org/10.48550/arxiv.1212.5183	preprint	January 2012
Renormalization of Entanglement Entropy and the Gravitational Effective Action Cooperman, Joshua H.; Luty, Markus A. arXiv https://doi.org/10.48550/arxiv.1302.1878	text	January 2013
On Spacetime Entanglement Myers, Robert C.; Pourhasan, Razieh; Smolkin, Michael arXiv https://doi.org/10.48550/arxiv.1304.2030	text	January 2013
Cool horizons for entangled black holes Maldacena, Juan; Susskind, Leonard arXiv https://doi.org/10.48550/arxiv.1306.0533	text	January 2013
Quantum corrections to holographic entanglement entropy Faulkner, Thomas; Lewkowycz, Aitor; Maldacena, Juan arXiv https://doi.org/10.48550/arxiv.1307.2892	text	January 2013
Entropy on a null surface for interacting quantum field theories and the Bousso bound Bousso, Raphael; Casini, Horacio; Fisher, Zachary arXiv https://doi.org/10.48550/arxiv.1406.4545	text	January 2014
Entanglement Equilibrium and the Einstein Equation Jacobson, Ted arXiv https://doi.org/10.48550/arxiv.1505.04753	text	January 2015
Holographic entropy inequalities and gapped phases of matter Bao, Ning; Cao, ChunJun; Walter, Michael arXiv https://doi.org/10.48550/arxiv.1507.05650	text	January 2015
Tensor Networks from Kinematic Space Czech, Bartlomiej; Lamprou, Lampros; McCandlish, Samuel arXiv https://doi.org/10.48550/arxiv.1512.01548	text	January 2015
Comments on Jacobson's "Entanglement equilibrium and the Einstein equation" Casini, Horacio; Galante, Damian A.; Myers, Robert C. arXiv https://doi.org/10.48550/arxiv.1601.00528	text	January 2016
Holographic duality from random tensor networks Hayden, Patrick; Nezami, Sepehr; Qi, Xiao-Liang arXiv https://doi.org/10.48550/arxiv.1601.01694	text	January 2016
Entropy Bounds and Black Hole Remnants Bekenstein, Jacob D. arXiv https://doi.org/10.48550/arxiv.gr-qc/9307035	text	January 1993
Von Neumann Algebra Automorphisms and Time-Thermodynamics Relation in General Covariant Quantum Theories Connes, A.; Rovelli, C. arXiv https://doi.org/10.48550/arxiv.gr-qc/9406019	text	January 1994
A Quantum Bousso Bound Strominger, Andrew; Thompson, David arXiv https://doi.org/10.48550/arxiv.hep-th/0303067	text	January 2003
The World as a Hologram Susskind, L. arXiv https://doi.org/10.48550/arxiv.hep-th/9409089	text	January 1994
The Large N Limit of Superconformal Field Theories and Supergravity Maldacena, Juan M. arXiv https://doi.org/10.48550/arxiv.hep-th/9711200	text	January 1997
A Covariant Entropy Conjecture Bousso, Raphael arXiv https://doi.org/10.48550/arxiv.hep-th/9905177	text	January 1999
Spectral Gap and Exponential Decay of Correlations Hastings, Matthew B.; Koma, Tohru arXiv https://doi.org/10.48550/arxiv.math-ph/0507008	text	January 2005
Fault-tolerant quantum computation by anyons Kitaev, A. Yu. arXiv https://doi.org/10.48550/arxiv.quant-ph/9707021	text	January 1997

Cited By (33)

Spacetime as a Quantum Many-Body System Oriti, D. Many-body Approaches at Different Scales https://doi.org/10.1007/978-3-319-72374-7_29	book	January 2018
Locality from the Spectrum Cotler, Jordan S.; Penington, Geoffrey R.; Ranard, Daniel H. Communications in Mathematical Physics, Vol. 368, Issue 3 https://doi.org/10.1007/s00220-019-03376-w	journal	February 2019
Reality and Super-Reality: Properties of a Mathematical Multiverse McKenzie, Alan Axiomathes, Vol. 30, Issue 4 https://doi.org/10.1007/s10516-019-09466-7	journal	November 2019
Information Graph Flow: A Geometric Approximation of Quantum and Statistical Systems Vanchurin, Vitaly Foundations of Physics, Vol. 48, Issue 6 https://doi.org/10.1007/s10701-018-0166-z	journal	May 2018
Quantum-First Gravity Giddings, Steven B. Foundations of Physics, Vol. 49, Issue 3 https://doi.org/10.1007/s10701-019-00239-1	journal	February 2019
Towards space from Hilbert space: finding lattice structure in finite-dimensional quantum systems Pollack, Jason; Singh, Ashmeet Quantum Studies: Mathematics and Foundations, Vol. 6, Issue 2 https://doi.org/10.1007/s40509-018-0176-8	journal	December 2018
Entanglement of single-photons and chiral phonons in atomically thin WSe2 Chen, Xiaotong; Lu, Xin; Dubey, Sudipta Nature Physics, Vol. 15, Issue 3 https://doi.org/10.1038/s41567-018-0366-7	journal	December 2018
Curved backgrounds in emergent gravity Chaurasia, Shikha; Erlich, Joshua; Zhou, Yiyu Classical and Quantum Gravity, Vol. 35, Issue 11 https://doi.org/10.1088/1361-6382/aabac0	journal	May 2018
Group field theory and tensor networks: towards a Ryu–Takayanagi formula in full quantum gravity Chirco, Goffredo; Oriti, Daniele; Zhang, Mingyi Classical and Quantum Gravity, Vol. 35, Issue 11 https://doi.org/10.1088/1361-6382/aabf55	journal	May 2018
Stochastic emergent quantum gravity Erlich, Joshua Classical and Quantum Gravity, Vol. 35, Issue 24 https://doi.org/10.1088/1361-6382/aaeb55	journal	November 2018
Towards bulk metric reconstruction from extremal area variations Bao, Ning; Cao, ChunJun; Fischetti, Sebastian Classical and Quantum Gravity, Vol. 36, Issue 18 https://doi.org/10.1088/1361-6382/ab377f	journal	August 2019
Spacetime granularity from finite-dimensionality of local observable algebras Raasakka, Matti Classical and Quantum Gravity, Vol. 37, Issue 4 https://doi.org/10.1088/1361-6382/ab5eb0	journal	January 2020
Reflections on the information paradigm in quantum and gravitational physics Höhn, Philipp Andres Journal of Physics: Conference Series, Vol. 880 https://doi.org/10.1088/1742-6596/880/1/012014	journal	August 2017
Operational locality in global theories Krämer, Lea; del Rio, Lídia Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 376, Issue 2123 https://doi.org/10.1098/rsta.2017.0321	journal	May 2018
Black holes in the quantum universe Giddings, Steven B. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 377, Issue 2161 https://doi.org/10.1098/rsta.2019.0029	journal	November 2019
Quantum decimation in Hilbert space: Coarse graining without structure Singh, Ashmeet; Carroll, Sean M. Physical Review A, Vol. 97, Issue 3 https://doi.org/10.1103/physreva.97.032111	journal	March 2018
Cosmic equilibration: A holographic no-hair theorem from the generalized second law Carroll, Sean M.; Chatwin-Davies, Aidan Physical Review D, Vol. 97, Issue 4 https://doi.org/10.1103/physrevd.97.046012	journal	February 2018
Fate of the Hoop Conjecture in Quantum Gravity Anzà, Fabio; Chirco, Goffredo Physical Review Letters, Vol. 119, Issue 23 https://doi.org/10.1103/physrevlett.119.231301	journal	December 2017
Covariant information theory and emergent gravity Vanchurin, Vitaly International Journal of Modern Physics A, Vol. 33, Issue 34 https://doi.org/10.1142/s0217751x18450197	journal	December 2018
The Hilbert space of quantum gravity is locally finite-dimensional Bao, Ning; Carroll, Sean M.; Singh, Ashmeet International Journal of Modern Physics D https://doi.org/10.1142/s0218271817170131	journal	October 2017
Operational locality in global theories Krämer, Lea; Del Rio, Lídia ETH Zurich https://doi.org/10.3929/ethz-b-000272705	text	January 2018
Group Field theory and Tensor Networks: towards a Ryu-Takayanagi formula in full quantum gravity Chirco, Goffredo; Oriti, Daniele; Zhang, Mingyi arXiv https://doi.org/10.48550/arxiv.1701.01383	text	January 2017
Operational locality in global theories Kraemer, Lea; del Rio, Lidia arXiv https://doi.org/10.48550/arxiv.1701.03280	text	January 2017
Emergent Gravity of Fractons: Mach's Principle Revisited Pretko, Michael arXiv https://doi.org/10.48550/arxiv.1702.07613	text	January 2017
Cosmic Equilibration: A Holographic No-Hair Theorem from the Generalized Second Law Carroll, Sean M.; Chatwin-Davies, Aidan arXiv https://doi.org/10.48550/arxiv.1703.09241	text	January 2017
Covariant Information Theory and Emergent Gravity Vanchurin, Vitaly arXiv https://doi.org/10.48550/arxiv.1707.05004	text	January 2017
Curved Backgrounds in Emergent Gravity Chaurasia, Shikha; Erlich, Joshua; Zhou, Yiyu arXiv https://doi.org/10.48550/arxiv.1710.07262	text	January 2017
Bulk Entanglement Gravity without a Boundary: Towards Finding Einstein's Equation in Hilbert Space Cao, ChunJun; Carroll, Sean M. arXiv https://doi.org/10.48550/arxiv.1712.02803	text	January 2017
Quantum-first gravity Giddings, Steven B. arXiv https://doi.org/10.48550/arxiv.1803.04973	text	January 2018
Von Neumann entropy from unitarity Boes, P.; Eisert, J.; Gallego, R. arXiv https://doi.org/10.48550/arxiv.1807.08773	text	January 2018
Entanglement of single-photons and chiral phonons in atomically thin WSe$_2$ Chen, Xiaotong; Lu, Xin; Dubey, Sudipta arXiv https://doi.org/10.48550/arxiv.1808.09984	text	January 2018
Towards Bulk Metric Reconstruction from Extremal Area Variations Bao, Ning; Cao, ChunJun; Fischetti, Sebastian arXiv https://doi.org/10.48550/arxiv.1904.04834	text	January 2019
Black holes in the quantum universe Giddings, Steven B. arXiv https://doi.org/10.48550/arxiv.1905.08807	text	January 2019

Similar Records

Space from Hilbert space: Recovering geometry from bulk entanglement

Journal Article · Fri Jan 27 00:00:00 EST 2017 · Physical Review D · OSTI ID:1536213

Cao, ChunJun; Carroll, Sean M.; Michalakis, Spyridon

Bulk entanglement gravity without a boundary: Towards finding Einstein’s equation in Hilbert space

Journal Article · Tue Apr 03 00:00:00 EDT 2018 · Physical Review. D. · OSTI ID:1536213

Cao, ChunJun; Carroll, Sean M.

Towards space from Hilbert space: finding lattice structure in finite-dimensional quantum systems

Journal Article · Tue Dec 04 00:00:00 EST 2018 · Quantum Studies: Mathematics and Foundations · OSTI ID:1536213

Pollack, Jason; Singh, Ashmeet

Related Subjects

Astronomy & Astrophysics
Physics

Title: Space from Hilbert space: Recovering geometry from bulk entanglement

Citation Formats

References (82)

Cited By (33)

Similar Records

Related Subjects