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Explore a research seminar on quantum chaos diagnostics through the lens of process tensor theory. Learn about the projected process ensemble, a novel framework for analyzing quantum systems under repeated interventions that provides increasingly fine-grained probes of chaotic behavior. Discover how the first moment of this ensemble encompasses established chaos quantifiers including the Alicki-Fannes quantum dynamical entropy, butterfly flutter fidelity, and spatiotemporal entanglement. Examine characteristic entanglement structures within higher moments that can sharply distinguish chaotic from integrable dynamics, addressing limitations of quantum dynamical and spatiotemporal entropies. Review extensive numerical simulations across various spin-chain models spanning non-interacting, interacting-integrable, chaotic, and many-body localized regimes. Understand how this work illuminates chaos fingerprints on spatiotemporal correlations in quantum stochastic processes and provides a unified analytical framework for both unitary and monitored many-body dynamics.
