Built on

W. Israel, “Thermo-field dynamics of black holes,” Physics Letters A 57
1976
Earlier work this paper cites.
M. Fannes, B. Nachtergaele, and R. F. Werner, “Finitely correlated states on quantum spin chains,” Communications in Mathematical Physics 144
1992
Earlier work this paper cites.
Maximo Banados, Claudio Teitelboim, and Jorge Zanelli, “The Black hole in three-dimensional space-time,” Phys. Rev. Lett. 69
1992
Earlier work this paper cites.
Stellan Östlund and Stefan Rommer, “Thermodynamic limit of density matrix renormalization,” Phys. Rev. Lett. 75
1995
Earlier work this paper cites.
Juan Martin Maldacena, “The Large N limit of superconformal field theories and supergravity,” Int. J. Theor. Phys. 38
1998
Earlier work this paper cites.
Edward Witten, “Anti-de Sitter space and holography,” Adv. Theor. Math. Phys. 2
1998
Earlier work this paper cites.
S.S. Gubser, I.R. Klebanov, and A.M. Polyakov, “Gauge theory correlators from non-critical string theory,” Physics Letters B 428
1998
Earlier work this paper cites.
B. M. Terhal, M. Horodecki, D. W. Leung, and D. P. DiVincenzo, “The entanglement of purification,” Journal of Mathematical Physics 43
2002
Earlier work this paper cites.
Juan Martin Maldacena, “Eternal black holes in anti-de Sitter,” JHEP 04
2003
Earlier work this paper cites.
F. Verstraete, J. J. García-Ripoll, and J. I. Cirac, “Matrix product density operators: Simulation of finite-temperature and dissipative systems,” Phys. Rev. Lett. 93
2004
Earlier work this paper cites.
Adrian E. Feiguin and Steven R. White, “Finite-temperature density matrix renormalization using an enlarged hilbert space,” Phys. Rev. B 72
2005
Earlier work this paper cites.
Shinsei Ryu and Tadashi Takayanagi, “Holographic derivation of entanglement entropy from AdS/CFT,” Phys. Rev. Lett. 96
2006
Earlier work this paper cites.
Sergey Bravyi, David Fattal, and Daniel Gottesman, “Ghz extraction yield for multipartite stabilizer states,” Journal of Mathematical Physics 47
2006
Earlier work this paper cites.

Similar

G. Vidal, “Classical simulation of infinite-size quantum lattice systems in one spatial dimension,” Phys. Rev. Lett. 98
2007
Cited alongside, same era.
Veronika E. Hubeny, Mukund Rangamani, and Tadashi Takayanagi, “A Covariant holographic entanglement entropy proposal,” JHEP 07
Original
2007
Cited alongside, same era.
G. Evenbly and G. Vidal, “Algorithms for entanglement renormalization,” Phys. Rev. B 79
2009
Cited alongside, same era.
I. Peschel and V. Eisler, “Reduced density matrices and entanglement entropy in free lattice models,” Journal of Physics A Mathematical General 42
Original
2009
Cited alongside, same era.
U. Schollwöck, “The density-matrix renormalization group in the age of matrix product states,” Annals of Physics 326
Original
2011

Then

Ian A. Morrison and Matthew M. Roberts, “Mutual information between thermo-field doubles and disconnected holographic boundaries,” JHEP 07
Original
2013
Later among the works it cites.
Patrick Hayden, Matthew Headrick, and Alexander Maloney, “Holographic Mutual Information is Monogamous,” Phys. Rev. D87
Original
2013
Later among the works it cites.
Matthew Headrick, Veronika E. Hubeny, Albion Lawrence, and Mukund Rangamani, “Causality & holographic entanglement entropy,” JHEP 12
Original
2014
Later among the works it cites.
Aron C. Wall, “Maximin Surfaces, and the Strong Subadditivity of the Covariant Holographic Entanglement Entropy,” Class. Quant. Grav. 31
Original
2014
Later among the works it cites.
S. Bagchi and A. K. Pati, “Monogamy, polygamy, and other properties of entanglement of purification,” Phys. Rev. A 91

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2017

Entanglement of purification: from spin chains to holography

Nguyen, Phuc, Devakul, Trithep, Halbasch, Matthew G. et al.

Understand

Purification is a powerful technique in quantum physics whereby a mixed quantum state is extended to a pure state on a larger system.

This process is not unique, and in systems composed of many degrees of freedom, one natural purification is the one with minimal entanglement.
Here we study the entropy of the minimally entangled purification, called the entanglement of purification, in three model systems: an Ising spin chain, conformal field theories holographically dual to Einstein gravity, and random stabilizer tensor networks.
We conjecture values for the entanglement of purification in all these models, and we support our conjectures with a variety of numerical and analytical results.

Built on

W. Israel, “Thermo-field dynamics of black holes,” Physics Letters A 57
1976
Earlier work this paper cites.
M. Fannes, B. Nachtergaele, and R. F. Werner, “Finitely correlated states on quantum spin chains,” Communications in Mathematical Physics 144
1992
Earlier work this paper cites.
Maximo Banados, Claudio Teitelboim, and Jorge Zanelli, “The Black hole in three-dimensional space-time,” Phys. Rev. Lett. 69
1992
Earlier work this paper cites.
Stellan Östlund and Stefan Rommer, “Thermodynamic limit of density matrix renormalization,” Phys. Rev. Lett. 75
1995
Earlier work this paper cites.
Juan Martin Maldacena, “The Large N limit of superconformal field theories and supergravity,” Int. J. Theor. Phys. 38
1998
Earlier work this paper cites.
Edward Witten, “Anti-de Sitter space and holography,” Adv. Theor. Math. Phys. 2
1998
Earlier work this paper cites.
S.S. Gubser, I.R. Klebanov, and A.M. Polyakov, “Gauge theory correlators from non-critical string theory,” Physics Letters B 428
1998
Earlier work this paper cites.
B. M. Terhal, M. Horodecki, D. W. Leung, and D. P. DiVincenzo, “The entanglement of purification,” Journal of Mathematical Physics 43
2002
Earlier work this paper cites.
Juan Martin Maldacena, “Eternal black holes in anti-de Sitter,” JHEP 04
2003
Earlier work this paper cites.
F. Verstraete, J. J. García-Ripoll, and J. I. Cirac, “Matrix product density operators: Simulation of finite-temperature and dissipative systems,” Phys. Rev. Lett. 93
2004
Earlier work this paper cites.
Adrian E. Feiguin and Steven R. White, “Finite-temperature density matrix renormalization using an enlarged hilbert space,” Phys. Rev. B 72
2005
Earlier work this paper cites.
Shinsei Ryu and Tadashi Takayanagi, “Holographic derivation of entanglement entropy from AdS/CFT,” Phys. Rev. Lett. 96
2006
Earlier work this paper cites.
Sergey Bravyi, David Fattal, and Daniel Gottesman, “Ghz extraction yield for multipartite stabilizer states,” Journal of Mathematical Physics 47
2006
Earlier work this paper cites.

Similar

G. Vidal, “Classical simulation of infinite-size quantum lattice systems in one spatial dimension,” Phys. Rev. Lett. 98
2007
Cited alongside, same era.
Veronika E. Hubeny, Mukund Rangamani, and Tadashi Takayanagi, “A Covariant holographic entanglement entropy proposal,” JHEP 07
Original
2007
Cited alongside, same era.
G. Evenbly and G. Vidal, “Algorithms for entanglement renormalization,” Phys. Rev. B 79
2009
Cited alongside, same era.
I. Peschel and V. Eisler, “Reduced density matrices and entanglement entropy in free lattice models,” Journal of Physics A Mathematical General 42
Original
2009
Cited alongside, same era.
U. Schollwöck, “The density-matrix renormalization group in the age of matrix product states,” Annals of Physics 326
Original
2011

Then

Ian A. Morrison and Matthew M. Roberts, “Mutual information between thermo-field doubles and disconnected holographic boundaries,” JHEP 07
Original
2013
Later among the works it cites.
Patrick Hayden, Matthew Headrick, and Alexander Maloney, “Holographic Mutual Information is Monogamous,” Phys. Rev. D87
Original
2013
Later among the works it cites.
Matthew Headrick, Veronika E. Hubeny, Albion Lawrence, and Mukund Rangamani, “Causality & holographic entanglement entropy,” JHEP 12
Original
2014
Later among the works it cites.
Aron C. Wall, “Maximin Surfaces, and the Strong Subadditivity of the Covariant Holographic Entanglement Entropy,” Class. Quant. Grav. 31
Original
2014
Later among the works it cites.
S. Bagchi and A. K. Pati, “Monogamy, polygamy, and other properties of entanglement of purification,” Phys. Rev. A 91

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

Cited alongside, same era.

Tadashi Takayanagi, “Holographic Dual of BCFT,” Phys. Rev. Lett. 107

Original

2011

Cited alongside, same era.

Shiang Yong Looi and Robert B. Griffiths, “Tripartite entanglement in qudit stabilizer states and application in quantum error correction,” Phys. Rev. A 84

2011

Cited alongside, same era.

Brian Swingle, “Entanglement Renormalization and Holography,” Phys. Rev. D86

Original

2012

Cited alongside, same era.

Bartlomiej Czech, Joanna L. Karczmarek, Fernando Nogueira, and Mark Van Raamsdonk, “The Gravity Dual of a Density Matrix,” Class. Quant. Grav. 29

Original

2012

Cited alongside, same era.

Pasquale Calabrese, John Cardy, and Erik Tonni, “Entanglement negativity in quantum field theory,” Phys. Rev. Lett. 109

Original

2012

Cited alongside, same era.

Veronika E. Hubeny, Henry Maxfield, Mukund Rangamani, and Erik Tonni, “Holographic entanglement plateaux,” JHEP 08

Original

2013

Cited alongside, same era.

C Karrasch, J H Bardarson, and J E Moore, “Reducing the numerical effort of finite-temperature density matrix renormalization group calculations,” New Journal of Physics 15

2013

Cited alongside, same era.

Original

2015