Built on

W. F. Stinespring, “Positive functions on c*-algebras,” Proceedings of the American Mathematical Society
1955
Earlier work this paper cites.
J. W. York, Jr., “Role of conformal three geometry in the dynamics of gravitation,” Phys. Rev. Lett. 28 (1972) 1082–1085
1972
Earlier work this paper cites.
G. W. Gibbons and S. W. Hawking, “Cosmological Event Horizons, Thermodynamics, and Particle Creation,” Phys. Rev. D15 (1977) 2738–2751
1977
Earlier work this paper cites.
L. Bombelli, R. K. Koul, J. Lee, and R. D. Sorkin, “A Quantum Source of Entropy for Black Holes,” Phys. Rev. D34 (1986) 373–383
1986
Earlier work this paper cites.
M. Srednicki, “Entropy and area,” Phys. Rev. Lett. 71 (1993) 666–669 , arXiv:hep-th/9303048 [hep-th]
1993
Earlier work this paper cites.
G. Hayward, “Gravitational action for space-times with nonsmooth boundaries,” Phys. Rev. D47 (1993) 3275–3280
1993
Earlier work this paper cites.
D. Brill and G. Hayward, “Is the gravitational action additive?,” Phys. Rev. D50 (1994) 4914–4919 , arXiv:gr-qc/9403018 [gr-qc]
1994
Earlier work this paper cites.
D. Aharonov, A. Kitaev, and N. Nisan, “Quantum circuits with mixed states,” in Proceedings of the Thirtieth Annual ACM Symposium on Theory of Computing
1998
Earlier work this paper cites.
R. Emparan, C. V. Johnson, and R. C. Myers, “Surface terms as counterterms in the AdS/CFT correspondence,” Phys. Rev. D60 (1999) 104001 , arXiv:hep-th/9903238 [hep-th]
1999
Earlier work this paper cites.
C. R. Graham and E. Witten, “Conformal anomaly of submanifold observables in AdS/CFT correspondence,” Nucl. Phys. B546 (1999) 52–64 , arXiv:hep-th/9901021 [hep-th]
1999
Earlier work this paper cites.
C. R. Graham and E. Witten, “Conformal anomaly of submanifold observables in AdS / CFT correspondence,” Nucl. Phys. B546 (1999) 52–64 , arXiv:hep-th/9901021 [hep-th]
1999
Earlier work this paper cites.
S. de Haro, S. N. Solodukhin, and K. Skenderis, “Holographic reconstruction of space-time and renormalization in the AdS/CFT correspondence,” Commun. Math. Phys. 217 (2001) 595–622 , arXiv:hep-th/0002230 [hep-th]
2001
Earlier work this paper cites.
K. Skenderis, “Lecture notes on holographic renormalization,” Class. Quant. Grav. 19 (2002) 5849–5876 , arXiv:hep-th/0209067 [hep-th]
2002
Earlier work this paper cites.
M. Kruczenski, “A Note on twist two operators in N=4 SYM and Wilson loops in Minkowski signature,” JHEP 12 (2002) 024 , arXiv:hep-th/0210115 [hep-th]
2002
Earlier work this paper cites.
S. Ryu and T. Takayanagi, “Holographic derivation of entanglement entropy from AdS/CFT,” Phys. Rev. Lett. 96 (2006) 181602 , arXiv:hep-th/0603001 [hep-th]
2006
Earlier work this paper cites.
S. Ryu and T. Takayanagi, “Aspects of Holographic Entanglement Entropy,” JHEP 08 (2006) 045 , arXiv:hep-th/0605073 [hep-th]
2006
Earlier work this paper cites.
M. A. Nielsen, “A geometric approach to quantum circuit lower bounds,” Quantum Info. Comput
2006
Earlier work this paper cites.
M. A. Nielsen, M. R. Dowling, M. Gu, and A. C. Doherty, “Quantum computation as geometry,” Science 311 no.~5764, (2006) 1133–1135 , arXiv:quant-ph/0603161 [quant-ph]
2006
Earlier work this paper cites.
V. E. Hubeny, M. Rangamani, and T. Takayanagi, “A Covariant holographic entanglement entropy proposal,” JHEP 07 (2007) 062 , arXiv:0705.0016 [hep-th]
Original
2007
Earlier work this paper cites.

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2016

Comments on Holographic Complexity

Carmi, Dean, Myers, Robert C., Rath, Pratik

Understand

We study two recent conjectures for holographic complexity: the complexity=action conjecture and the complexity=volume conjecture.

In particular, we examine the structure of the UV divergences appearing in these quantities, and show that the coefficients can be written as local integrals of geometric quantities in the boundary.
We also consider extending these conjectures to evaluate the complexity of the mixed state produced by reducing the pure global state to a specific subregion of the boundary time slice.
The UV divergences in this subregion complexity have a similar geometric structure, but there are also new divergences associated with the geometry of the surface enclosing the boundary region of interest.

Built on

W. F. Stinespring, “Positive functions on c*-algebras,” Proceedings of the American Mathematical Society
1955
Earlier work this paper cites.
J. W. York, Jr., “Role of conformal three geometry in the dynamics of gravitation,” Phys. Rev. Lett. 28 (1972) 1082–1085
1972
Earlier work this paper cites.
G. W. Gibbons and S. W. Hawking, “Cosmological Event Horizons, Thermodynamics, and Particle Creation,” Phys. Rev. D15 (1977) 2738–2751
1977
Earlier work this paper cites.
L. Bombelli, R. K. Koul, J. Lee, and R. D. Sorkin, “A Quantum Source of Entropy for Black Holes,” Phys. Rev. D34 (1986) 373–383
1986
Earlier work this paper cites.
M. Srednicki, “Entropy and area,” Phys. Rev. Lett. 71 (1993) 666–669 , arXiv:hep-th/9303048 [hep-th]
1993
Earlier work this paper cites.
G. Hayward, “Gravitational action for space-times with nonsmooth boundaries,” Phys. Rev. D47 (1993) 3275–3280
1993
Earlier work this paper cites.
D. Brill and G. Hayward, “Is the gravitational action additive?,” Phys. Rev. D50 (1994) 4914–4919 , arXiv:gr-qc/9403018 [gr-qc]
1994
Earlier work this paper cites.
D. Aharonov, A. Kitaev, and N. Nisan, “Quantum circuits with mixed states,” in Proceedings of the Thirtieth Annual ACM Symposium on Theory of Computing
1998
Earlier work this paper cites.
R. Emparan, C. V. Johnson, and R. C. Myers, “Surface terms as counterterms in the AdS/CFT correspondence,” Phys. Rev. D60 (1999) 104001 , arXiv:hep-th/9903238 [hep-th]
1999
Earlier work this paper cites.
C. R. Graham and E. Witten, “Conformal anomaly of submanifold observables in AdS/CFT correspondence,” Nucl. Phys. B546 (1999) 52–64 , arXiv:hep-th/9901021 [hep-th]
1999
Earlier work this paper cites.
C. R. Graham and E. Witten, “Conformal anomaly of submanifold observables in AdS / CFT correspondence,” Nucl. Phys. B546 (1999) 52–64 , arXiv:hep-th/9901021 [hep-th]
1999
Earlier work this paper cites.
S. de Haro, S. N. Solodukhin, and K. Skenderis, “Holographic reconstruction of space-time and renormalization in the AdS/CFT correspondence,” Commun. Math. Phys. 217 (2001) 595–622 , arXiv:hep-th/0002230 [hep-th]
2001
Earlier work this paper cites.
K. Skenderis, “Lecture notes on holographic renormalization,” Class. Quant. Grav. 19 (2002) 5849–5876 , arXiv:hep-th/0209067 [hep-th]
2002
Earlier work this paper cites.
M. Kruczenski, “A Note on twist two operators in N=4 SYM and Wilson loops in Minkowski signature,” JHEP 12 (2002) 024 , arXiv:hep-th/0210115 [hep-th]
2002
Earlier work this paper cites.
S. Ryu and T. Takayanagi, “Holographic derivation of entanglement entropy from AdS/CFT,” Phys. Rev. Lett. 96 (2006) 181602 , arXiv:hep-th/0603001 [hep-th]
2006
Earlier work this paper cites.
S. Ryu and T. Takayanagi, “Aspects of Holographic Entanglement Entropy,” JHEP 08 (2006) 045 , arXiv:hep-th/0605073 [hep-th]
2006
Earlier work this paper cites.
M. A. Nielsen, “A geometric approach to quantum circuit lower bounds,” Quantum Info. Comput
2006
Earlier work this paper cites.
M. A. Nielsen, M. R. Dowling, M. Gu, and A. C. Doherty, “Quantum computation as geometry,” Science 311 no.~5764, (2006) 1133–1135 , arXiv:quant-ph/0603161 [quant-ph]
2006
Earlier work this paper cites.
V. E. Hubeny, M. Rangamani, and T. Takayanagi, “A Covariant holographic entanglement entropy proposal,” JHEP 07 (2007) 062 , arXiv:0705.0016 [hep-th]
Original
2007
Earlier work this paper cites.