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Untangling entanglement and chaos

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How does classical chaos affect the generation of quantum entanglement? What signatures of chaos exist at the quantum level and how can they be quantified? These questions have puzzled physicists for a couple of decades now. We answer these questions in spin systems by analytically establishing a connection between entanglement generation and a measure of delocalization of a quantum state in such systems. While delocalization is a generic feature of quantum chaotic systems, it is more nuanced in regular systems. We explore when the quantum dynamics mimics a localized classical trajectory, and find criteria to quantify Bohr's correspondence principle in periodically driven spin systems. These criteria are typically violated in a deep quantum regime due to delocalized evolution. Using our criteria, we establish that entanglement is a signature of chaos only in a semiclassical regime. Our work provides a new approach to analyzing quantum chaos and designing systems that can efficiently generate entanglement. This work has been done in collaboration with Prof. Shohini Ghose.

References: arXiv:1806.10545 (2018) and PRE 97, 052209 (2018).