Entanglement in Time: A Quasiprobability Perspective

As Schrödinger famously emphasized, entanglement is not merely 
a feature but the defining characteristic of quantum mechanics, marking 
its fundamental departure from classical physics. Conventionally, 
entanglement is defined with respect to partitions of Hilbert space on 
equal-time slices. In this talk, I introduce a finite-dimensional notion 
of timelike entanglement defined via multi-time correlation functions. 
Using a local orthonormal operator basis, this construction can be 
expressed as a generalized response tensor, leading to an extension of 
the conventional density matrix with support across multiple times—the 
generalized spacetime density kernel (GSDK). The associated 
quasiprobability distribution provides a generalization of the 
well-known Kirkwood–Dirac distribution. Next, as an example, in the 
Rosenzweig–Porter model, I show that timelike entanglement entropies and 
timelike entanglement spectra of the spacetime kernel sharply probe 
eigenvector ergodicity across localized, fractal, and ergodic regimes, 
quantified via timelike Tsallis entropies, entanglement p-imagitivity, 
and a kernel negativity defined by the negative spectral weight of its 
Hermitian part, whose time-averaged behavior tracks the 
ergodic–fractal–localized crossover.