Localizable Entanglement Achieves Universal Scaling at Critical Measurement Probability
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Researchers are increasingly focused on measurement-induced phase transitions (MIPTs), and a new study spearheaded by Sourav Manna, Arul Lakshminarayan, and Vaibhav Madhok, all from the Department of Physics at the Indian Institute of Technology Madras, proposes a novel way to characterise these transitions.
The team identifies ‘localizable entanglement’ as an order parameter for MIPTs, demonstrating universal scaling behaviour consistent with existing research and offering a clear link to classical percolation theory. Significantly, their findings reveal an intrinsic length scale within these transitions, diverging at a critical measurement probability, and provide an operational interpretation relating MIPTs to the teleportation of quantum information , opening doors for experimentally verifying redistribution across the transition using a proposed two-ancilla protocol.
Localizable Entanglement Defines Measurement-Induced Phase Transitions in Quantum Scientists have identified localizable entanglement (LE) as a crucial order parameter for measurement-induced phase transitions (MIPT), offering a new lens through which to understand these complex quantum phenomena. The research team demonstrated that LE exhibits universal finite-size scaling, with critical exponents aligning with previously established MIPT results and providing a clear connection to classical percolation theory, a surprising and insightful parallel. Remarkably, experiments show LE decays exponentially with distance within the area-law phase, contrasting sharply with its essentially constant behaviour in the volume-law phase, thereby revealing an intrinsic length scale, denoted as ξE, that diverges precisely at the critical measurement probability, pc. This discovery establishes a quantifiable measure of how far quantum information can propagate before being lost to measurements, offering a powerful tool for characterizing these transitions. The study unveils that while classical percolation describes successful transport across a network, MIPT, as characterised by LE, can be interpreted as quantifying the degree of quantum teleportation possible between nodes in a quantum circuit. Building on this insight, the researchers proposed a novel two-ancilla protocol, designed to provide an experimentally accessible readout of entanglement redistribution across the transition, a significant step towards practical verification of their findings. This protocol leverages the unique properties of monitored quantum circuits, where the interplay between unitary dynamics and projective measurements drives the observed phase transitions.
The team exploited the stabilizer, graph-state correspondence within random Clifford circuits to compute LE exactly across varying system sizes and measurement rates, providing robust and reliable data. Their results definitively show that LE falls off exponentially with distance in the area-law phase, a previously unobserved phenomenon, but remains remarkably flat in the volume-law phase, solidifying the definition of the intrinsic length scale ξE. This length scale, diverging at the critical measurement probability pc, provides an operational interpretation: ξE measures the spatial extent over which entanglement can be concentrated through local operations. To probe the MIPT transition, the scientists employed a reference qubit initially maximally entangled with a site in the circuit, observing its behaviour under hybrid measurement-unitary dynamics. A finite LE between the reference and the system confirms the volume-law phase, while its vanishing indicates the area-law phase, with the transition becoming sharper as system size increases. Furthermore, the research introduces a second reference qubit, initially unentangled, and entangles it with the first after the monitored evolution, a clever technique to assess system connectivity. The resulting concurrence between the two references faithfully detects the MIPT, even without direct access to the system, offering a low-overhead, experimentally feasible method for probing the transition using only two-qubit measurements. Together, these results provide both an operational definition of entanglement correlation length through LE and a monogamy-based probe of measurement-induced phases, uniting percolation-based geometric connectivity, information theory, and experimental possibilities in the study of entanglement dynamics in monitored quantum systems.
Local Entanglement Quantifies Measurement-Induced Phase Transitions in many-body Scientists identified the localizable entanglement (LE) as an order parameter to characterise measurement-induced phase transitions (MIPT). The research team engineered a method to quantify the maximum entanglement concentrated between two qubits by performing local measurements on the remaining qubits, defining LEij = max M X s psE( ψij s), where E represents the entanglement measured by the von Neumann entropy of the reduced density matrix. This operational definition connects MIPTs to classical percolation, offering a novel interpretation of MIPTs as quantifying teleportation between nodes in a quantum circuit. To probe this, researchers developed a two-ancilla protocol providing an experimentally accessible readout of redistribution across the transition, utilising an om gate after monitored evolution. The resulting concurrence between two reference qubits reflects system connectivity; monogamy exponentially suppresses entanglement in the volume-law phase, while direct entanglement emerges in the area-law phase, allowing detection of the MIPT solely from two-qubit measurements. Experiments employed (1 + 1)-dimensional monitored brickwall quantum circuits composed of discrete time layers of random unitary gates and projective measurements, averaging over independent realisations to obtain all quantities. The study pioneered the construction of an order parameter, R, defined as the largest separation ratio |i −j|/(L −1) for which LE remains non-zero, with R = maxi,j |i −j| L −1 : LEij 0. Researchers then calculated ⟨R⟩ as a function of measurement probability p for random Clifford brickwall circuits of varying system sizes L, observing curves crossing near pc = 0.16, signalling the transition from the entangling to the disentangling phase. This crossing demonstrated that ⟨R⟩ captures the change in the spatial extent of LE across the transition, exhibiting non-analytic critical behaviour at the transition point. Furthermore, the team analysed the entanglement correlation function ⟨CLE(r; p)⟩, finding exponential decay in the area-law phase (p pc) enabling extraction of the entanglement correlation length ξE(p), while approaching a constant for p. 👉 More information 🗞 Localizable Entanglement as an Order Parameter for Measurement-Induced Phase Transitions 🧠 ArXiv: https://arxiv.org/abs/2601.14185 Tags: