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Probing scrambling and operator size distributions using random mixed states and local measurements

Philip Daniel Blocher, Karthik Chinni, Sivaprasad Omanakuttan and Pablo M. Poggi

Article (2024)

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Abstract

The dynamical spreading of quantum information through a many-body system, typically called scrambling, is a complex process that has proven to be essential to describe many properties of out-of-equilibrium quantum systems. Scrambling can, in principle, be fully characterized via the use of out-of-time-ordered correlation functions, which are notoriously hard to access experimentally. In this work, we put forward an alternative toolbox of measurement protocols to experimentally probe scrambling by accessing properties of the operator size probability distribution, which tracks the size of the support of observables in a many-body system over time. Our measurement protocols require the preparation of separable mixed states together with local operations and measurements, and combine the tools of randomized operations, a modern development of near-term quantum algorithms, with the use of mixed states, a standard tool in NMR experiments. We demonstrate how to efficiently probe the probability-generating function of the operator distribution and discuss the challenges associated with obtaining the moments of the operator distribution. We further show that manipulating the initial state of the protocol allows us to directly obtain the individual elements of the distribution for small system sizes.

Subjects: 3100 Physics > 3100 Physics
Department: Department of Engineering Physics
Funders: NSERC / CRSNG, U.S. Department of Energy - Office of Science - National Quantum Information Science Research Centers - Quantum Systems Accelerator, US National Science Foundation, Québec - Ministère de l’Économie et de l’Innovation, AFOSR
Grant number: PHY-2116246, FA9550-181-1-0064
PolyPublie URL: https://publications.polymtl.ca/57909/
Journal Title: Physical review research (vol. 6, no. 1)
Publisher: American Physical Society
DOI: 10.1103/physrevresearch.6.013309
Official URL: https://doi.org/10.1103/physrevresearch.6.013309
Date Deposited: 14 May 2024 09:41
Last Modified: 25 May 2024 04:54
Cite in APA 7: Blocher, P. D., Chinni, K., Omanakuttan, S., & Poggi, P. M. (2024). Probing scrambling and operator size distributions using random mixed states and local measurements. Physical review research, 6(1), 03309 (15 pages). https://doi.org/10.1103/physrevresearch.6.013309

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