Entanglement is not enough

By L. Susskind. 2014

456 citations recorded by the source corpus.

This is the written version of a lecture given at KITP in Oct 2014 on Black Holes and quantum complexity. I've included (in boldface) various questions that came up during the lecture and discussions the following day, as well as the quantitative calculations that form the basis of the arguments.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/e8f841ff250801231bb0f423e062ec189c8492b7

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Citations in the corpus

Chaos in quantum channels (2015, background): “However, the implication does not work in the other direction: since the late-time values of I(A : C), I(A : D), and I3(A : C : D) approach Haar-scrambled values, entanglement is not enough [52] to diagnose typicality (in the Haar-random sense).”
Quantum extremal islands made easy. Part II. Black holes on the brane (2020, background): “On a related note, one might also study the complexity of these brane configurations, for example, using the higher-dimensional bulk to probe holographic complexity conjectures [145–148], e.”
Quantum Entanglement in Neural Network States (2017, background): “Yet, as has been realized in a number of diﬀerent physical contexts, the entanglement entropy cannot capture the full entanglement structure of the system [96–101].”
Noether charge, black hole volume, and complexity (2016, background): “. A commonly encountered statement found in the literature is the fact that the time derivative of the complexity should be proportional to the product of the temperature and entropy (see for example [39]): C˘_ TS (5.1) The relation above is quite appealing from the viewpoint of quantum circuits: on”
Krylov complexity in saddle-dominated scrambling (2022, background): “Holographically, similar behavior has been conjectured for the volume of the interior of the black hole at late times [58, 59].”
Complexity and entanglement for thermofield double states (2018, background): “This implies that “entanglement (entropy) is not enough” [14] to capture the dynamics behind the horizon, and in particular that there must be some other quantity in the dual field theory which encodes this late-time evolution of the wormhole interior.”
Circuit complexity for coherent states (2018, background): “ions of holographic entanglement entropy [9{11]. However, it has become clear that holographic entanglement entropy is not able to probe the bulk spacetime far behind the event horizon of black holes [12,13]. Inspired by this problem, Susskind { 1 { [13{15] proposed the study of new bulk observables”
On volumes of subregions in holography and complexity (2016, background): “In [24–31] there were two important conjectures made about how to compute complexity in holography2.”
Holographic complexity in Vaidya spacetimes. Part I (2018, background): “However, it was recently observed that holographic entanglement entropy will not capture certain features of the late time behaviour of eternal black hole geometries or of the dual boundary thermal states [24].”
Holographic complexity in Vaidya spacetimes. Part II (2018, background): “Further, as is evident from the holographic results or can be argued on more general grounds [11, 14], the rate is expected to be proportional to the energy of the system.”
Divergences in holographic complexity (2016, background): “y) could be identied with the volume of a maximal volume spacelike slice in the bulk, ending on the given boundary slice. This will be referred to as the CV conjecture. This was further developed in [4,5]. More recently, it was conjectured that the complexity is related instead to the action of a Wh”
Comments on holographic complexity (2016, methodology): “These coefficients also contain dimensionless parameters characterizing the underlying CFT, e.g., CT ∼ Ld−1/GN in the present case where the bulk is described by Einstein gravity.11 The leading divergence appearing with the CV duality is proportional to the volume of the boundary time slice, i.e., C”