Free Bosons Purify Faster than Free Fermions in 0D

In quantum many-body systems subject to random unitary gates and local measurements, the purification dynamics

concerns how the entanglement entropy decreases starting from an initially mixed state. Different phases of purification

dynamics can be distinguished by whether the system purifies in the long time limit. In this talk, we discuss the long-

time purification dynamics of a 0D free bosonic system with N boson modes. This system evolves under alternating

random Gaussian unitary rotations and partial Gaussian measurements. Through analytical study and numerical

simulation using the Gaussian-state formalism, we show that such a system always purifies in the long-time limit, and

determine an upper bound for the purification rate of the system. For example, we find that for one-mode Gaussian

measurements, the entanglement entropy exponentially decays with a characteristic time scale of 1/N. We note that

an analogous model for free fermions has already been studied in [Quantum 5, 382 (2021)]. It was shown that the

entanglement entropy in this free fermion system decays as ∼ N/t at long times, where N is the number of fermionic

modes and t counts the number of time-steps taken through the circuit. Hence, we show that free bosons purify faster

than free fermions in 0D.