Issue |
EPL
Volume 147, Number 3, August 2024
|
|
---|---|---|
Article Number | 38002 | |
Number of page(s) | 7 | |
Section | Quantum information | |
DOI | https://doi.org/10.1209/0295-5075/ad5b17 | |
Published online | 22 August 2024 |
Operator growth and spread complexity in open quantum systems
1 School of Physics, University College Dublin - Belfield, Dublin 4, Ireland
2 Centre for Quantum Engineering, Science, and Technology, University College Dublin Belfield, Dublin 4, Ireland
3 Department of Physics, University of Maryland - Baltimore County, Baltimore, MD 21250, USA
4 National Quantum Laboratory - College Park, MD 20740, USA
Received: 9 April 2024
Accepted: 24 June 2024
Commonly, the notion of “quantum chaos” refers to the fast scrambling of information throughout complex quantum systems undergoing unitary evolution. Motivated by the Krylov complexity and the operator growth hypothesis, we demonstrate that the entropy of the population distribution for an operator in time is a useful way to capture the complexity of the internal information dynamics of a system when subject to an environment and is, in principle, agnostic to the specific choice of operator basis. We demonstrate its effectiveness for the Sachdev-Ye-Kitaev (SYK) model, examining the dynamics of the system in both its Krylov basis and the basis of operator strings. We prove that the former basis minimises spread complexity while the latter is an eigenbasis for high dissipation. In both cases, we probe the long-time dynamics of the model and the phenomenological effects of decoherence on the complexity of the dynamics.
© 2024 The author(s)
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