Chaos in quantum channels

By P. Hosur, Xiao-Liang Qi, Daniel A. Roberts, B. Yoshida. 2015

670 citations recorded by the source corpus.

A bstractWe study chaos and scrambling in unitary channels by considering their entanglement properties as states. Using out-of-time-order correlation functions to diagnose chaos, we characterize the ability of a channel to process quantum information. We show that the generic decay of such correlators implies that any input subsystem must have near vanishing mutual information with almost all partitions of the output. Additionally, we propose the negativity of the tripartite information of the channel as a general diagnostic of scrambling. This measures the delocalization of information and is closely related to the decay of out-of-time-order correlators. We back up our results with numerics in two non-integrable models and analytic results in a perfect tensor network model of chaotic time evolution. These results show that the butterfly effect in quantum systems implies the information-theoretic definition of scrambling.

Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/160128a7ecda981618da0e2e36362de326ac6071

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Citations in the corpus

Measuring out-of-time-order correlators on a nuclear magnetic resonance quantum simulator (2016, background): “This relates to the fact that the information does scramble in a nonintegrable system [11].”
Coarse-grained dynamics of operator and state entanglement (2018, neutral): “[10] Pavan Hosur, Xiao-Liang Qi, Daniel A.”
Measurement-Induced Phase Transitions in the Dynamics of Entanglement (2018, background): “[7] Pavan Hosur, Xiao-Liang Qi, Daniel A.”
Emergent statistical mechanics of entanglement in random unitary circuits (2018, background): “The entanglement entropy is a fundamental quantity whose dynamics remains nontrivial even in the absence of any conventional hydrodynamic modes [10, 11, 15– 26].”
Scrambling and thermalization in a diffusive quantum many-body system (2016, background): “[10] Pavan Hosur, Xiao-Liang Qi, Daniel A.”
Entanglement Membrane in Chaotic Many-Body Systems (2019, background): “The effective statistical mechanics of this membrane determine the production of entanglement after a quantum quench, the spreading of quantum operators, and other aspects of the “scrambling” [7, 8, 11, 19–34] of quantum information.”
Disentangling Scrambling and Decoherence via Quantum Teleportation (2018, methodology): “Our above definition of scrambling is required to hold for all local operators, but a slightly more coarse-grained characterization of scrambling (and one which is easier to probe experimentally) can be achieved via the averaged OTOC [15]:”
Diffusive Hydrodynamics of Out-of-Time-Ordered Correlators with Charge Conservation (2017, neutral): “For translation-invariant systems they have been studied in weakly coupled [42] local quantum field theories [15,16,18,43,44], in models for black hole scrambling [12,28,45], and more recently in local random circuits [25,26].”
Slow scrambling in disordered quantum systems (2016, background): “This feature i s also responsible for the logarithmic growth of entanglemen t in the MBL phase [ 42, 45]; these are in fact related statements [31].”
Measurement-driven entanglement transition in hybrid quantum circuits (2019, background): “As for unitary Hamiltonian dynamics, there is a notion of chaos in such Floquet circuits, as diagnosed by the entanglement growth [49, 50], the operator growth (and butterfly effect in out-of-time-order correlator) [51], the level spacing statistics and the spectral form factor [45, 46, 48, 52], etc”
Universal diffusion in incoherent black holes (2016, background): “where vB is the velocity of the ‘butterfly effect’ [9–18] and C is a constant that depended on the universality class of theory.”
Bounding the space of holographic CFTs with chaos (2016, background): “Recently, it has been argued that a kind of “average” measure of chaotic behavior of general 2d CFTs can be directly related to the second Rényi entropy, S2, for two disjoint intervals separated in space and time [12].”