Binding Complexity and the Cost of Entanglement

I will discuss the relation of quantum complexity, especially in the geometric Nielsen's formulation, to entanglement. In particular I will show that there is a class of complexity measures, called “binding complexity” defined by a certain choice of penalty factors, which is closely related to entanglement and Renyi entropies, and characterize the minimal complexity needed to produce a certain amount of entanglement. The talk is based on the paper arXiv:2311.04277