Unpredictability and entanglement in open quantum systems

authored by: Hendrik Weimer, Javad Kazemi
Abstract: We investigate dynamical many-body systems capable of universal computation, which leads to their properties being unpredictable unless the dynamics is simulated from the beginning to the end. Unpredictable behavior can be quantitatively assessed in terms of a data compression of the states occurring during the time evolution, which is closely related to their Kolmogorov complexity. We analyze a master equation embedding of classical cellular automata and demonstrate the existence of a phase transition between predictable and unpredictable behavior as a function of the random noise introduced by the embedding. We then turn to have this dynamics competing with a second process inducing quantum fluctuations and dissipatively driving the system to a highly entangled steady state. Strikingly, for intermediate strength of the quantum fluctuations, we find that both unpredictability and quantum entanglement can coexist even in the long time limit. Finally, we show that the required many-body interactions for the cellular automaton embedding can be efficiently realized within a variational quantum simulator platform based on ultracold Rydberg atoms with high fidelity.
Organisation(s): Institute of Theoretical Physics
QuantumFrontiers
CRC 1227 Designed Quantum States of Matter (DQ-mat)
Type: Article
Journal: New Journal of Physics
Volume: 25
ISSN: 1367-2630
Publication date: 15.09.2023
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: General Physics and Astronomy
Electronic version(s): http://arxiv.org/abs/2106.07673v1 (Access: Open)
https://doi.org/10.1088/1367-2630/acf151 (Access: Open)

BibTeX

@article{01595fcf4567449893c206b80a38f2c9,
title = "Unpredictability and entanglement in open quantum systems",
abstract = " We investigate dynamical many-body systems capable of universal computation, which leads to their properties being unpredictable unless the dynamics is simulated from the beginning to the end. Unpredictable behavior can be quantitatively assessed in terms of a data compression of the states occurring during the time evolution, which is closely related to their Kolmogorov complexity. We analyze a master equation embedding of classical cellular automata and demonstrate the existence of a phase transition between predictable and unpredictable behavior as a function of the random noise introduced by the embedding. We then turn to have this dynamics competing with a second process inducing quantum fluctuations and dissipatively driving the system to a highly entangled steady state. Strikingly, for intermediate strength of the quantum fluctuations, we find that both unpredictability and quantum entanglement can coexist even in the long time limit. Finally, we show that the required many-body interactions for the cellular automaton embedding can be efficiently realized within a variational quantum simulator platform based on ultracold Rydberg atoms with high fidelity. ",
keywords = "quant-ph, cond-mat.stat-mech, elementary cellular automata, computational unpredictability, variational quantum simulation",
author = "Hendrik Weimer and Javad Kazemi",
note = "Funding Information: The authors acknowledge fruitful discussion with R van Bijnen on variational quantum simulation. This work was funded by the Volkswagen Foundation, by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) within SFB 1227 (DQ-mat, project A04), SPP 1929 (GiRyd), and under Germanys Excellence Strategy—EXC-2123 QuantumFrontiers - 390837967.",
year = "2023",
month = sep,
day = "15",
doi = "10.1088/1367-2630/acf151",
language = "English",
volume = "25",
journal = "New Journal of Physics",
issn = "1367-2630",
publisher = "IOP Publishing Ltd.",
number = "9",
}