Localizable Entanglement as an Order Parameter for Measurement-Induced Phase Transitions

• URL: http://arxiv.org/abs/2601.14185v1
• Date: Tue, 20 Jan 2026 17:43:33 GMT
• Title: Localizable Entanglement as an Order Parameter for Measurement-Induced Phase Transitions
• Authors: Sourav Manna, Arul Lakshminarayan, Vaibhav Madhok,
• Abstract summary: Localizable entanglement (LE) is an order parameter for measurement-induced phase transitions.<n>We find that LE decays exponentially with distance in the area-law phase as opposed to being essentially constant for the volume-law phase.<n>We propose a two-ancilla protocol that provides an experimentally accessible readout of entanglement redistribution across the transition.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We identify localizable entanglement (LE) as an order parameter for measurement-induced phase transitions (MIPT). LE exhibits universal finite-size scaling with critical exponents that match previous MIPT results and gives a nice operational interpretation connecting MIPTs to classical percolation. Remarkably, we find that LE decays exponentially with distance in the area-law phase as opposed to being essentially constant for the volume-law phase thereby, discover an intrinsic length scale $ξ_E$ that diverges at the critical measurement probability $p_c$. While classical percolation transition captures successful transport across a network, MIPT as characterized by LE can be interpreted as quantifying the amount of quantum teleportation between two given nodes in a quantum circuit. Building on this insight, we propose a two-ancilla protocol that provides an experimentally accessible readout of entanglement redistribution across the transition.

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