Built on

S. Dutta and T. Faulkner, A canonical purification for the entanglement wedge cross-section
Original
1905
Earlier work this paper cites.
G. Penington, Entanglement wedge reconstruction and the information paradox
Original
1905
Earlier work this paper cites.
A. Almheiri, N. Engelhardt, D. Marolf, and H. Maxfield, The entropy of bulk quantum fields and the entanglement wedge of an evaporating black hole
Original
1905
Earlier work this paper cites.
Y. Kusuki, J. Kudler-Flam, and S. Ryu, Derivation of holographic negativity in AdS 3 /CFT 2
Original
1907
Earlier work this paper cites.
A. Almheiri, R. Mahajan, J. Maldacena, and Y. Zhao, The Page curve of Hawking radiation from semiclassical geometry
Original
1908
Earlier work this paper cites.
J. Sorce, Holographic entanglement entropy is cutoff-covariant
Original
1908
Earlier work this paper cites.
C. Akers, A. Levine, and S. Leichenauer, Large breakdowns of entanglement wedge reconstruction
Original
1908
Earlier work this paper cites.
N. Bao and N. Cheng, Multipartite reflected entropy
Original
1909
Earlier work this paper cites.
C. Akers and P. Rath, Entanglement wedge cross sections require tripartite entanglement
Original
1911
Earlier work this paper cites.
G. Penington, S. H. Shenker, D. Stanford, and Z. Yang, Replica wormholes and the black hole interior
Original
1911
Earlier work this paper cites.
S. Colin-Ellerin, V. E. Hubeny, B. E. Niehoff, and J. Sorce, Large-d phase transitions in holographic mutual information
Original
1911
Earlier work this paper cites.
C. Akers, N. Engelhardt, G. Penington, and M. Usatyuk, Quantum maximin surfaces
Original
1912
Earlier work this paper cites.
McGraw-Hill Book Company, 1953
H. Bateman, Higher transcendental functions [volumes i-iii] · 1953
Earlier work this paper cites.
L. Accardi and A. Frigerio, Markovian cocycles
1983
Earlier work this paper cites.
D. Petz, Sufficient subalgebras and the relative entropy of states of a von Neumann algebra
1986
Earlier work this paper cites.
M. A. Nielsen and I. Chuang, Quantum computation and quantum information
2002
Earlier work this paper cites.
P. Bueno and H. Casini, Reflected entropy, symmetries and free fermions
Original
2003
Earlier work this paper cites.
P. Hayden, R. Jozsa, D. Petz, and A. Winter, Structure of states which satisfy strong subadditivity of quantum entropy with equality
2004
Earlier work this paper cites.
J. A. Mingo and A. Nica, Annular noncrossing permutations and partitions, and second-order asymptotics for random matrices
2004
Earlier work this paper cites.
S. Ryu and T. Takayanagi, Holographic derivation of entanglement entropy from AdS/CFT
2006
Earlier work this paper cites.
S. Ryu and T. Takayanagi, Aspects of Holographic Entanglement Entropy
2006
Earlier work this paper cites.
V. Chandrasekaran, M. Miyaji, and P. Rath, Including contributions from entanglement islands to the reflected entropy
Original
2006
Earlier work this paper cites.
X. Dong and H. Wang, Enhanced corrections near holographic entanglement transitions: a chaotic case study
Original
2006
Earlier work this paper cites.
D. Marolf, S. Wang, and Z. Wang, Probing phase transitions of holographic entanglement entropy with fixed area states
Original
2006
Earlier work this paper cites.

Similar

M. Headrick and T. Takayanagi, Holographic proof of the strong subadditivity of entanglement entropy
Original
2007
Cited alongside, same era.
V. E. Hubeny, M. Rangamani, and T. Takayanagi, A Covariant holographic entanglement entropy proposal
Original
2007
Cited alongside, same era.
Cambridge University Press, 2007
A. Marden, Outer Circles: An introduction to hyperbolic 3-manifolds · 2007
Cited alongside, same era.
C. Akers and G. Penington, Leading order corrections to the quantum extremal surface prescription
Original
2008
Cited alongside, same era.
P. Bueno and H. Casini, Reflected entropy for free scalars
Original
2008
Cited alongside, same era.

Then

N. Bao, S. Nezami, H. Ooguri, B. Stoica, J. Sully, and M. Walter, The holographic entropy cone
Original
2015
Later among the works it cites.
O. Fawzi and R. Renner, Quantum conditional mutual information and approximate Markov chains
Original
2015
Later among the works it cites.
D. L. Jafferis, A. Lewkowycz, J. Maldacena, and S. J. Suh, Relative entropy equals bulk relative entropy
Original
2016
Later among the works it cites.
X. Dong, A. Lewkowycz, and M. Rangamani, Deriving covariant holographic entanglement
Original
2016
Later among the works it cites.
X. Dong, D. Harlow, and A. C. Wall, Reconstruction of bulk operators within the entanglement wedge in gauge-gravity duality

Beyond the bibliography

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

Open on alphaXiv

alphaXiv is searching for related work…

Reading the bibliography…

2021

The Markov gap for geometric reflected entropy

Hayden, Patrick, Parrikar, Onkar, Sorce, Jonathan

Understand

The reflected entropy $S_R(A:B)$ of a density matrix $\rho_{AB}$ is a bipartite correlation measure lower-bounded by the quantum mutual information $I(A:B)$.

In holographic states satisfying the quantum extremal surface formula, where the reflected entropy is related to the area of the entanglement wedge cross-section, there is often an order-$N^2$ gap between $S_R$ and $I$.
We provide an information-theoretic interpretation of this gap by observing that $S_R - I$ is related to the fidelity of a particular Markov recovery problem that is impossible in any state whose entanglement wedge cross-section has a nonempty boundary; for this reason, we call the quantity $S_R - I$ the Markov gap.
We then prove that for time-symmetric states in pure AdS$_3$ gravity, the Markov gap is universally lower bounded by $\log(2) \ell_{\text{AdS}}/2 G_N$ times the number of endpoints of the cross-section.