How dynamical Quantum memories forget

Motivated by recent work showing that a quantum error correcting code can be generated by hybrid dynamics of unitaries and measurements, a team of researchers has studied the long time behavior of such systems.

They demonstrated that even in the “mixed” phase, a maximally mixed initial density matrix is purified on a time scale equal to the Hilbert space dimension (i.e., exponential in system size), albeit with noisy dynamics at intermediate times which they connected to Dyson Brownian motion.

In contrast, they showed that free fermion systems — i.e., ones where the unitaries are generated by quadratic Hamiltonians and the measurements are of fermion bilinears — purify in a time quadratic in the system size. In particular, a volume law phase for the entanglement entropy cannot be sustained in a free fermion system.

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