Built on

M. Ghodrati, X.-M. Kuang, B. Wang, C.-Y. Zhang and Y.-T. Zhou, Aspects of holographic entanglement at finite temperature and chemical potential , JHEP 2019
Original
1902
Earlier work this paper cites.
J. Sorce, Holographic entanglement entropy is cutoff-covariant , 1908.02297
Original
1908
Earlier work this paper cites.
E. Størmer, Symmetric states of infinite tensor products of c ∗ c^{*} -algebras , J. Funct. Anal. 3
1969
Earlier work this paper cites.
R. L. Hudson and G. R. Moody, Locally normal symmetric states and an analogue of de Finetti’s theorem , Probability Theory and Related Fields 33
1976
Earlier work this paper cites.
A. Strominger, The Inverse Dimensional Expansion in Quantum Gravity , Phys. Rev. D24
1981
Earlier work this paper cites.
G. A. Raggio and R. F. Werner, Quantum statistical mechanics of general mean field systems , Helvetica Physica Acta 62
1989
Earlier work this paper cites.
M. R. Dowling, A. C. Doherty and S. D. Bartlett, Energy as an entanglement witness for quantum many-body systems , Phys. Rev. A 70
2004
Earlier work this paper cites.
R. König and R. Renner, A de Finetti representation for finite symmetric quantum states , J. Math. Phys. 46
2005
Earlier work this paper cites.
S. Ryu and T. Takayanagi, Aspects of holographic entanglement entropy , JHEP 2006
2006
Earlier work this paper cites.
V. E. Hubeny, M. Rangamani and T. Takayanagi, A covariant holographic entanglement entropy proposal , JHEP 2007
Original
2007
Earlier work this paper cites.
M. Christandl, R. König, G. Mitchison and R. Renner, One-and-a-half quantum de Finetti theorems , Comm. Math. Phys. 273
2007
Earlier work this paper cites.
M. M. Wolf, F. Verstraete, M. B. Hastings and J. I. Cirac, Area Laws in Quantum Systems: Mutual Information and Correlations , Phys. Rev. Lett. 100
Original
2008
Earlier work this paper cites.
F. G. Brandao, M. Christandl and J. Yard, A quasipolynomial-time algorithm for the quantum separability problem , Proceedings of ACM Symposium on Theory of Computation (2011) 343 [ 1011.2751 ]
Original
2011
Earlier work this paper cites.

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2019

Large-$d$ phase transitions in holographic mutual information

Colin-Ellerin, Sean, Hubeny, Veronika E., Niehoff, Benjamin E. et al.

Understand

In the AdS/CFT correspondence, the entanglement entropy of subregions in the boundary CFT is conjectured to be dual to the area of a bulk extremal surface at leading order in $G_N$ in the holographic limit.

Under this dictionary, distantly separated regions in the CFT vacuum state have zero mutual information at leading order, and only attain nonzero mutual information at this order when they lie close enough to develop significant classical and quantum correlations.
Previously, the separation at which this phase transition occurs for equal-size ball-shaped regions centered at antipodal points on the boundary was known analytically only in $3$ spacetime dimensions.
Inspired by recent explorations of general relativity at large-$d$, we compute the separation at which the phase transition occurs analytically in the limit of infinitely many spacetime dimensions, and find that distant regions cannot develop large correlations without collectively occupying the entire volume of the boundary theory.

Built on

M. Ghodrati, X.-M. Kuang, B. Wang, C.-Y. Zhang and Y.-T. Zhou, Aspects of holographic entanglement at finite temperature and chemical potential , JHEP 2019
Original
1902
Earlier work this paper cites.
J. Sorce, Holographic entanglement entropy is cutoff-covariant , 1908.02297
Original
1908
Earlier work this paper cites.
E. Størmer, Symmetric states of infinite tensor products of c ∗ c^{*} -algebras , J. Funct. Anal. 3
1969
Earlier work this paper cites.
R. L. Hudson and G. R. Moody, Locally normal symmetric states and an analogue of de Finetti’s theorem , Probability Theory and Related Fields 33
1976
Earlier work this paper cites.
A. Strominger, The Inverse Dimensional Expansion in Quantum Gravity , Phys. Rev. D24
1981
Earlier work this paper cites.
G. A. Raggio and R. F. Werner, Quantum statistical mechanics of general mean field systems , Helvetica Physica Acta 62
1989
Earlier work this paper cites.
M. R. Dowling, A. C. Doherty and S. D. Bartlett, Energy as an entanglement witness for quantum many-body systems , Phys. Rev. A 70
2004
Earlier work this paper cites.
R. König and R. Renner, A de Finetti representation for finite symmetric quantum states , J. Math. Phys. 46
2005
Earlier work this paper cites.
S. Ryu and T. Takayanagi, Aspects of holographic entanglement entropy , JHEP 2006
2006
Earlier work this paper cites.
V. E. Hubeny, M. Rangamani and T. Takayanagi, A covariant holographic entanglement entropy proposal , JHEP 2007
Original
2007
Earlier work this paper cites.
M. Christandl, R. König, G. Mitchison and R. Renner, One-and-a-half quantum de Finetti theorems , Comm. Math. Phys. 273
2007
Earlier work this paper cites.
M. M. Wolf, F. Verstraete, M. B. Hastings and J. I. Cirac, Area Laws in Quantum Systems: Mutual Information and Correlations , Phys. Rev. Lett. 100
Original
2008
Earlier work this paper cites.
F. G. Brandao, M. Christandl and J. Yard, A quasipolynomial-time algorithm for the quantum separability problem , Proceedings of ACM Symposium on Theory of Computation (2011) 343 [ 1011.2751 ]
Original
2011
Earlier work this paper cites.