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

TL;DR

This paper explores how long-range measurement-only circuits in one dimension can induce various entanglement phases and transitions, revealing new regimes of entanglement, information scrambling, and purification.

Contribution

It introduces a comprehensive phase diagram for long-range measurement-only Clifford circuits, connecting entanglement transitions to a long-range XX model and uncovering unique phases with coexisting entanglement and rapid purification.

Findings

Identified multiple entanglement phases requiring diverse probes beyond entropy.

Mapped entanglement transitions to a long-range XX model in a statistical mechanics framework.

Discovered structured circuits with coexisting volume-law entanglement and rapid, non-scrambling purification.

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.