Entanglement Entropy & Area Law

Measurement-induced phase transitions (Li et al 2018, Chan et al 2019): random unitary circuits evolve toward volume-law entanglement S~L (quantum information scrambling). Frequent measurements project the state, driving toward area-law S~const. The transition at p_c≈0.16 is a new type of quantum phase transition. Here we track bipartite entanglement using stabilizer entropy (simulated via correlation matrix).