Switchbacks and the Bridge to Nowhere

By L. Susskind, Ying Zhao. 2014

191 citations recorded by the source corpus.

This paper is in three parts: Part 1 explains the relevance of Einstein-Rosen bridges for one-sided black holes. Like their two-sided counterparts, one-sided black holes are connected to ERBs whose growth tracks the increasing complexity of the quantum state. Quantitative solutions for one-sided ERBs are presented in the appendix. Part 2 calls attention to the work of Nielsen and collaborators on the geometry of quantum complexity. This geometric formulation of complexity provides a valuable tool for studying the evolution of complexity for systems such as black holes. Part 3 applies the Nielsen approach to geometrize two related black hole quantum phenomena: the rapid mixing of information through fast-scrambling; and the time dependence of the complexity of precursors, in particular the switchback effect.

Subfields: Atomic and Molecular Physics, and Optics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/24e9fd87678c4c5b9dbbe3241ce612220a4c34b7

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Citations in the corpus

Chaos and complexity by design (2016, background): “While there is nice qualitative evidence for both of these proposals [67, 13, 65], missing is a direct understanding of computational complexity in systems that evolve continuously in time with a time-independent Hamiltonian.”
Second law of quantum complexity (2017, methodology): “• Hayden-Preskill circuits exhibit an effect called the switchback effect [2, 3].”
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”
Linear growth of quantum circuit complexity (2021, background): “However, a notion related to causal slices appears in the switchback effect in holography [12, 53, 57].”
Quantum complexity and negative curvature (2016, background): “The most striking evidence for the holographic duality between the complexity of the boundary theory and the size (volume or action) of the corresponding ERB in the bulk is provided by the switchback effect [2, 20].”
Holographic Complexity Equals Bulk Action? (2015, unknown): “(See also [1, 2, 4–8].”
Entanglement is not enough (2014, background): “Among these slices there is one of maximum spatial volume [7, 8].”
Holographic complexity in Vaidya spacetimes. Part II (2018, methodology): “The factor of two in the second term is the same one mentioned in footnote 9 of [19] and is due to the fact that K/2 gates act in a unit time step.”
Complexity of formation in holography (2016, background): “However, this problem was recently overcome with a careful analysis of the boundary terms which must be added to the (1)See [5, 11] for further details.”
Holographic complexity in Vaidya spacetimes. Part I (2018, background): “All of these results are in accord with the expectations and calculations presented in [52].”
Islands in Schwarzschild black holes (2020, background): “The calculation of that extremal surface resembles that of a holographic complexity (“complexity = volume” conjecture [34, 35]).”