Notes on time entanglement and pseudo-entropy

Understand

Following arXiv:2210.12963 [hep-th], we investigate aspects of the time evolution operator regarded as a density operator and associated entanglement-like structures in various quantum systems.

• These involve timelike separations and generically lead to complex-valued entropy, although there are interesting real subfamilies.
• There are many parallels and close relations with reduced transition matrices and pseudo-entropy, which we discuss and clarify.
• For instance, a related quantity involves the time evolution operator along with a projection onto some initial state, which amounts to analysing pseudo-entropy for the initial state and its time-evolved final state.