Abstract: The goal of this seminar is to provide an overview of our recent results. We will discuss connections between operator entanglement of the dynamics, OTOCs, and entropy production as introduced in [1]. Then we will discuss how to 'disentangle' contributions from decoherence vs. scrambling for open quantum systems [2]. How finite temperature 'regularized' OTOCs are related to spectral form factors and the purity of the time-evolved thermofield double state [3]. An intermezzo about quantum coherence and OTOCs of random diagonal unitaries [4]. A quick overview of an operator algebraic framework for scrambling that is useful for both closed and open quantum systems [5]. And finally how OTOCs behave in local non-Hermitian Hamiltonians [6] with some discussion of ongoing work.

References: [1] https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.126.030601

[2] https://journals.aps.org/pra/abstract/10.1103/PhysRevA.103.062214

[3] https://quantum-journal.org/papers/q-2022-06-27-746/

[4] https://journals.aps.org/prresearch/abstract/10.1103/PhysRevResearch.3.023214

[5] https://journals.aps.org/pra/abstract/10.1103/PhysRevA.107.042217

[6] https://arxiv.org/abs/2305.12054