Operator entanglement barrier in 1D quantum systems
The ‘operator entanglement’ is an indicator of the complexity of quantum operators, and of their approximability by Matrix Product Operators (MPO) in 1D quantum systems. I will discuss the ‘entanglement barrier’: the fact that the OE of a reduced density matrix initially grows linearly as entanglement builds up between the local degrees of freedom, then reaches a maximum, and ultimately decays to a small finite value as the reduced density matrix converges to a simple stationary state through standard thermalization mechanisms.
This ‘entanglement barrier’ can be obtained in various models, and it has recently been found in experimental data in the trapped ion setup of [Brydges et al., Science 364, 260 (2019)], by performing a new analysis of the data using the randomized measurement toolbox.
I will also briefly discuss the influence of chaotic vs. integrable dynamics, as well as dissipation, on the shape of the ‘entanglement barrier’.