We consider the time evolution of the gaps of the entanglement spectrum for a block of consecutive sites in finite transverse field Ising chains after sudden quenches of the magnetic field. We provide numerical evidence that, whenever we quench at or across the quantum critical point, the time evolution of the ratios of these gaps allows us to obtain universal information. They encode the low-lying gaps of the conformal spectrum of the Ising boundary conformal field theory describing the spatial bipartition within the imaginary time path integral approach to global quenches at the quantum critical point.

The fact that the computational cost of simulating a many-body quantum system on a computer increases with the amount of entanglement has been considered as the major bottleneck for simulating its out-of-equilibrium dynamics. Some aspects of the dynamics are, nevertheless, robust under appropriately devised approximations. Here we present a possible algorithm that allows to systematically approximate the equilibration value of local operators after a quantum quench. At the core of our proposal there is the idea to transform entanglement between distant parts of the system into mixture, and at the same time preserving the local reduced density matrices of the system. We benchmark the resulting algorithm by studying quenches of quadratic Fermionic Hamiltonians.

We consider two chains, each made of N independent oscillators, immersed in a common thermal bath and study the dynamics of their mutual quantum correlations in the thermodynamic, large-N limit. We show that dissipation and noise due to the presence of the external environment are able to generate collective quantum correlations between the two chains at the mesoscopic level. The created collective quantum entanglement between the two many-body systems turns out to be rather robust, surviving for asymptotically long times even for non vanishing bath temperatures.

A non-isolated physical system typically loses information to its environment, and when such loss is irreversible the evolution is said to be Markovian. Non-Markovian effects are studied by monitoring how information quantifiers, such as the distance between physical states, evolve in time. Here we show that the Fisher information metric emerges as the natural object to study in this context; we fully characterize the relation between its contractivity properties and Markovianity, both from the mathematical and operational point of view. We prove, for classical dynamics, that Markovianity is equivalent to the monotonous contraction of the Fisher metric at all points of the set of states. At the same time, operational witnesses of non-Markovianity based on the dilation of the Fisher distance cannot, in general, detect all non-Markovian evolutions, unless specific physical postprocessing is applied to the dynamics. Finally, we show for the first time that non-Markovian dilations of Fisher distance between states at any time correspond to backflow of information about the initial state of the dynamics at time 0, via Bayesian retrodiction. All the presented results can be lifted to the case of quantum dynamics by considering the standard CP-divisibility framework.