Entanglement and information scrambling in long-range measurement-only circuits

• URL: http://arxiv.org/abs/2604.22022v1
• Date: Thu, 23 Apr 2026 19:29:27 GMT
• Title: Entanglement and information scrambling in long-range measurement-only circuits
• Abstract summary: Measurement-only circuits provide a minimal setting in which repeated local projections can generate or suppress many-body entanglement.<n>We investigate entanglement and information transitions in one-dimensional measurement-only Clifford circuits with long-range two-qubit parity checks.<n>We find a phase in which volume-law and long-range entanglement coexists with rapid, size-independent purification of an ancilla qubit.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Measurement-only circuits provide a minimal setting in which repeated local projections can either generate or suppress many-body entanglement, giving rise to measurement-induced phase transitions and dynamical regimes, that might have no unitary counterpart. Here we investigate entanglement and information transitions in one-dimensional measurement-only Clifford circuits with long-range two-qubit parity checks. By tuning both the measurement range and density per layer, we uncover a broad set of phases whose classification requires probes beyond entanglement entropy, such as mutual information, tripartite mutual information, purification from an ancilla, and Bell-cluster statistics. We map phase diagrams using large-scale Clifford simulations for two protocols: a random-basis design in which each measurement is randomly chosen from $\lbrace XX,YY,ZZ \rbrace$, and a single-basis design in which the basis is fixed within each layer but varies between layers, hence introducing more structure to the circuit. We map the trajectory-averaged entanglement entropy to a two-dimensional statistical mechanics model by extending a replica-based method to random-basis measurement-only circuits, and show that a continuous-time limit yields an effective long-range XX hamiltonian in the steady state. This connection links the observed volume-law to sub-volume-law entanglement transition to the boundary between a continuous symmetry broken phase and a critical XY phase. Strikingly, in structured (single-basis) circuits we find a phase in which volume-law and long-range entanglement coexists with rapid, size-independent purification of an ancilla qubit, and the absence of scrambling, highlighting measurement-only circuits as a promising route to efficiently preparing highly entangled and technologically useful quantum states.

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