QG group meeting: Entanglement and complexity of squeezed states

Squeezed states have a wide range of applications in physics, ranging from Hawking radiation, adiabatic vacua in Cosmology to integrable condensed matter systems. I will introduce the underlying mathematical framework of a Kähler structure on phase space, which we can use to parametrize squeezed states in terms of linear complex structures. Our methods apply to both fermionic and bosonic systems, and I will discuss key advantages for the study of entanglement and time evolution.

Recently, we applied our methods to define circuit complexity of squeezed states where complexity refers to the quantum information notion quantifying the number of gates required to prepare a given state. Complexity has drawn increased to understand aspects of the AdS/CFT correspondence that cannot be captured by entanglement entropy, for instance the continued evolution of black hole interiors past the thermalization time. Defining circuit complexity on the field theory side is non-trivial and I will report on recent progress to define a geometric circuit complexity in the Lie group of symplectic transformations.