We identify localizable entanglement (LE) as an order parameter for measurement-induced phase transitions (MIPTs). 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 and, thereby, discover an intrinsic length scale ${\xi }_E$ 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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• Critical phenomena
• Phase transitions
• Quantum circuits
• Quantum phase transitions
• Quantum simulation
• Many-body techniques