ETD

• entanglement entropy
• integrable systems
• matrix product states
• measurement induced phase transition
• monitored quantum systems
• quantum cellular automaton
• quasiparticle ansatz

We investigate the entanglement dynamics of the Rule 54 quantum cellular automaton subject to stochastic projective measurements. Rule 54 is an interacting integrable model whose closed dynamics are exactly described by a semiclassical quasiparticle picture: entangled soliton pairs propagate ballistically and scatter elastically, generating entanglement at a rate determined analytically by the thermodynamic entropy density and the dressed quasiparticle velocity. We study how this picture is modified when measurements are interleaved with the unitary evolution, comparing two protocols that differ in their relationship to the conserved soliton charge.
For measurements in the computational basis (Z-basis), which commute with the conserved charge, we derive an exact analytical prediction for the entanglement decay: the quasiparticle ansatz is modified by a measurement-induced exponential envelope exp(−4γt) , where γ is the measurement rate. This prediction is validated through finite-size scaling collapse across system sizes and measurement rates, with excellent agreement between analytics and Matrix Product State simulations.
For measurements in the X-basis, which do not commute with the conserved charge, measurements act simultaneously as a source and a sink of entanglement through a quasiparticle reseeding mechanism. Our numerical results are consistent with a measurement-induced phase transition at a finite critical rate, in sharp contrast to the Z-basis case where any nonzero measurement rate drives the system to an area-law phase. A preliminary finite-size scaling analysis yields γc = 0.370 ± 0.004 (pc ≈ 0.31) and ν = 0.97 ± 0.03, though a complete characterization of the universality class requires larger system sizes.