Scrambling and Quantum Chaos Indicators from Long-time Properties of Operator Distributions
April 4, 2023 - S. Omanakuttan, K. Chinni. P. Blocher and P. M. Poggi
Scrambling and Quantum Chaos Indicators from Long-time Properties of Operator Distributions
When particles carrying quantum information interact with each other, the information spreads within the system and loses its local character. This process, typically called quantum information scrambling, underpins many fundamental phenomena in physics ranging from thermalization to radiation dynamics in black holes. Understanding how to diagnose and characterize this process is thus an outstanding challenge, and developing new intuitive ways to properly visualize and quantify different aspects of scrambling is desirable.
In a recent paper published in Physical Review A [1], researchers from CQuIC Sivaprasad Omanakuttan, Philip Blocher, and Pablo Poggi, together with CQuIC alumnus Karthik Chinni, have shown that a comprehensive analysis of quantum information scrambling can be achieved by studying so-called operator size distributions. These distributions can be defined for general quantum systems by introducing a coarse-graining in a suitable operator basis, leading to an input space which is much smaller than the full (exponentially large) Hilbert space. In the publication, the group showed show that the onset of quantum chaos can be identified in these systems by analyzing the long-time properties of operator size distributions. They observed that an enhancement of temporal fluctuations in the mean and variance of the distribution, together with deviations from the predictions arising from completely random evolution, are clear signatures of nonergodicity in the system. Similar signatures are seen in the properties of operator distributions for models of random circuits as non-Clifford gates are injected into the circuit.
Finally, the group’s study includes a formal analysis of the connection between operator size distributions and out-of-time-order correlators (OTOCs), the latter of which are particular correlation functions commonly used to diagnose quantum information scrambling. In this analysis, the group also comments on the cost of probing the coarse-grained operator distribution experimentally using these out-of-time-ordered correlators.
[1] S. Omanakuttan, K. Chinni. P. Blocher and P. M. Poggi. Scrambling and quantum chaos indicators from long-time properties of operator distributions, Phys. Rev. A 107, 032418 – Published 21 March 2023
