Built on

Addison-Wesley Publishing Company, Massachusetts, 1976
L. A. Santaló, Integral Geometry and Geometric Probability · 1976
Earlier work this paper cites.
M. Banados, C. Teitelboim and J. Zanelli, The Black hole in three-dimensional space-time , Phys. Rev. Lett. 69
1992
Earlier work this paper cites.
Addison-Wesley, Reading, Massachusetts, 1994
C. M. Papadimitriou, Computational complexity · 1994
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 , Physical Review Letters 96
2006
Earlier work this paper cites.
M. A. Nielsen, A geometric approach to quantum circuit lower bounds , Quantum Information and Computation 6
2006
Earlier work this paper cites.
R. C. Myers and A. Sinha, Seeing a c-theorem with holography , Phys. Rev. D82
Original
2010
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.
R. C. Myers and A. Sinha, Holographic c-theorems in arbitrary dimensions , JHEP 01
Original
2011
Earlier work this paper cites.
V. E. Hubeny, H. Maxfield, M. Rangamani and E. Tonni, Holographic entanglement plateaux , JHEP 08
Original
2013
Earlier work this paper cites.
N. Lashkari, M. B. McDermott and M. Van Raamsdonk, Gravitational dynamics from entanglement ’thermodynamics’ , JHEP 04
Original
2014
Earlier work this paper cites.
B. Czech and L. Lamprou, Holographic definition of points and distances , Phys. Rev. D90
Original
2014
Earlier work this paper cites.
V. Balasubramanian, B. D. Chowdhury, B. Czech, J. de Boer and M. P. Heller, Bulk curves from boundary data in holography , Phys. Rev. D89
Original
2014
Earlier work this paper cites.
M. Miyaji, T. Numasawa, N. Shiba, T. Takayanagi and K. Watanabe, Distance between Quantum States and Gauge-Gravity Duality , Phys. Rev. Lett. 115
Original
2015
Earlier work this paper cites.

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2018

Holographic Subregion Complexity from Kinematic Space

Abt, Raimond, Erdmenger, Johanna, Gerbershagen, Marius et al.

Understand

We consider the computation of volumes contained in a spatial slice of AdS$_3$ in terms of observables in a dual CFT.

Our main tool is kinematic space, defined either from the bulk perspective as the space of oriented bulk geodesics, or from the CFT perspective as the space of entangling intervals.
We give an explicit formula for the volume of a general region in the spatial slice as an integral over kinematic space.
For the region lying below a geodesic, we show how to write this volume purely in terms of entangling entropies in the dual CFT.