IFTiA seminar of Professor Michał P. Heller
We kindly invite you
to a seminar of
(Ghent University & Uniwersytet Jagielloński)
which will take place on
September 18th (Friday) on 12:15
in lecture hall 1.15.
Title of the seminar:
Entanglement in time and the complexity of quantum evolution: a holographic perspective.
Abstract: Can entanglement be meaningfully extended from regions of space to intervals of time, and how should we quantify the complexity of quantum evolution? I will explore these questions through two complementary developments in quantum field theory and holography. First, I will explain how spatial entanglement entropy can be continued into the timelike domain, and how replica correlation functions make this construction precise in two-dimensional conformal field theory. The resulting entropy is generally complex: operator ordering fixes its imaginary part, which reflects effective causal structure in the examples studied, while its gravitational description involves complex extremal surfaces. Second, I will discuss Krylov spread complexity, which measures how an evolving quantum state spreads in a basis generated by its Hamiltonian. For thermofield-double states-purifications of thermal states-this quantity can be reconstructed from the thermal partition function. Applying this construction to a theory dual to a three-dimensional black hole yields dynamics incompatible with the usual volume-based description of complexity, with evidence for quadratic rather than linear growth in the semiclassical late-time regime. I will explain how a generalized geometric construction can accommodate this behavior. Together, these developments provide concrete settings in which to ask what extensions of familiar quantum-information concepts actually measure, and how their interpretation is constrained by causality, dynamics and geometry.