Towards the fast scrambling conjecture

By Nima Lashkari, D. Stanford, M. B. Hastings, Tobias J. Osborne, Patrick M. Hayden. Journal of High Energy Physics, 2011

429 citations recorded by the source corpus.

Many proposed quantum mechanical models of black holes include highly non-local interactions. The time required for thermalization to occur in such models should reflect the relaxation times associated with classical black holes in general relativity. Moreover, the time required for a particularly strong form of thermalization to occur, sometimes known as scrambling, determines the time scale on which black holes should start to release information. It has been conjectured that black holes scramble in a time logarithmic in their entropy, and that no system in nature can scramble faster. In this article, we address the conjecture from two directions. First, we exhibit two examples of systems that do indeed scramble in logarithmic time: Brownian quantum circuits and the antiferromagnetic Ising model on a sparse random graph. Unfortunately, both fail to be truly ideal fast scramblers for reasons we discuss. Second, we use Lieb-Robinson techniques to prove a logarithmic lower bound on the scrambling time of systems with finite norm terms in their Hamiltonian. The bound holds in spite of any nonlocal structure in the Hamiltonian, which might permit every degree of freedom to interact directly with every other one.

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

View Paper: https://www.semanticscholar.org/paper/03e435eb6ed96353cdb1ca0d80067213fb13829d

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Citations in the corpus

Chaos, complexity, and random matrices (2017, background): “The suggestion that black holes are the fastest scramblers in nature [2, 3] has led to a new probe of chaos in quantum systems, namely the 4-point out-of-time-order correlation function (OTOC).”
Black holes and random matrices (2016, background): “There is no ensemble of Hamiltonians in this system so we want to describe the time averaged behavior of Z(β, t) as discussed in the previous section.”
Random Quantum Circuits (2022, methodology): “An example is the “Brownian circuit” (90, 91, 133, 236, 237): this is a Hamiltonian spin chain where the couplings fluctuate like white noise.”
Black holes: complementarity or firewalls? (2012, background): “This time scale has an interesting resonance with ideas from quantum information theory and from Matrix theory [6, 7, 8, 9], which suggest that it may actually be achieved.”
Black holes and the butterfly effect (2013, background): “In the subject of quantum information and black holes, such chaotic behavior has come to be referred to as “scrambling,” and it has been conjectured that black holes are the fastest scramblers in nature [8, 9, 10, 11].”
Second law of quantum complexity (2017, background): “The resulting “Brownian circuits” were discussed in [17].”
Computational complexity and black hole horizons (2014, background): “One can assume that the relevant black hole degrees of freedom are a system of qubits that interact in a way that makes the black hole a fast-scrambler [13][14][15].”
Unitary designs from statistical mechanics in random quantum circuits. (2019, background): “It has also been shown [33] that Brownian quantum circuits [34] form designs in O ( nk 10 ) depth, with the same dependence on k as in [2].”
Time Dependence of Hawking Radiation Entropy (2013, background): “Here I shall assume without proof that the fifth answer is correct and make an additional assumption of nearly maximal entanglement between the black hole and the Hawking radiation [186, 25] (with support from the later conjecture of fast scrambling [187, 188, 189, 190, 191]).”
Local random quantum circuits are approximate polynomial-designs: numerical results (2012, background): “Corollary 15 also shows that one dimensional parallel random circuits scramble [48, 57, 72] – making an initial localized bit of information inaccessible to an observer that only looks at sublinear sized regions – in linear time, confirming the expectation of Refs.”
Chaos and complexity by design (2016, methodology): “Finally, it’s a curious fact that for systems with time-dependent Hamiltonian ensembles (such as the random circuit models or the Brownian circuit of [5]) that we get an initial linear growth of the volume with T .”
Locality, Quantum Fluctuations, and Scrambling (2018, background): “BCC, as an extension of the single cluster version [46,47], describes the dynamics of clusters of N spins connected in a one-dimensional array (or more generally, connected according to any graph), similar to coupled SYK cluster models but with the couplings random in both space and time.”
Jerusalem Lectures on Black Holes and Quantum Information (2014, result): “It is also quite fast compared to what is expected for more conventional systems with comparable entropy, and in the aftermath of the Hayden and Preskill paper there was quite a bit of activity aimed at understanding what sorts of physical systems might realize this “fast scrambling” [56–59].”
A bound on chaos (2015, methodology): “A logarithmic scrambling time was conjectured for nonlocal Hamiltonian systems in [2, 3], and supported by a Lieb-Robinson bound in [15].”