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

TL;DR

This paper demonstrates that localizable entanglement serves as an effective order parameter for measurement-induced phase transitions, revealing universal scaling and a diverging length scale at criticality, with implications for quantum teleportation and experimental detection.

Contribution

It introduces localizable entanglement as a novel order parameter for MIPT, linking it to classical percolation and providing an experimentally accessible protocol.

Findings

LE exhibits universal finite-size scaling at MIPT

LE decays exponentially in the area-law phase

A diverging length scale $\xi_E$ is identified at the critical point

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 $\xi_E$ 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.