Page curves and typical entanglement in linear optics

Understand

Bosonic Gaussian states are a special class of quantum states in an infinite dimensional Hilbert space that are relevant to universal continuous-variable quantum computation as well as to near-term quantum sampling tasks such as Gaussian Boson Sampling.

• In this work, we study entanglement within a set of squeezed modes that have been evolved by a random linear optical unitary.
• We first derive formulas that are asymptotically exact in the number of modes for the R\'enyi-2 Page curve (the average R\'enyi-2 entropy of a subsystem of a pure bosonic Gaussian state) and the corresponding Page correction (the average information of the subsystem) in certain squeezing regimes.
• We then prove various results on the typicality of entanglement as measured by the R\'enyi-2 entropy by studying its variance.