Measurement-induced phase transitions on dynamical quantum trees

TL;DR

This paper analytically and numerically investigates measurement-induced phase transitions in qubit systems with tree-like spacetime interactions, revealing differences between real and forced measurements and proposing an experimental protocol.

Contribution

It introduces exactly solvable models for measurement-induced transitions with real measurements on qubits in tree structures, advancing understanding of their critical behavior.

Findings

Both real and forced measurements show a transition at a nontrivial measurement strength.

The real measurement case has a smaller entangling phase compared to forced measurements.

Entanglement scales exponentially near the transition, with different critical exponents.

Abstract

Monitored many-body systems fall broadly into two dynamical phases, ``entangling'' or ``disentangling'', separated by a transition as a function of the rate at which measurements are made on the system. Producing an analytical theory of this measurement-induced transition is an outstanding challenge. Recent work made progress in the context of tree tensor networks, which can be related to all-to-all quantum circuit dynamics with forced (postselected) measurement outcomes. So far, however, there are no exact solutions for dynamics of spin-1/2 degrees of freedom (qubits) with ``real'' measurements, whose outcome probabilities are sampled according to the Born rule. Here we define dynamical processes for qubits, with real measurements, that have a tree-like spacetime interaction graph, either collapsing or expanding the system as a function of time. The former case yields an exactly solvable measurement transition. We explore these processes analytically and numerically, exploiting the recursive structure of the tree. We compare the case of ``real'' measurements with the case of ``forced'' measurements. Both cases show a transition at a nontrivial value of the measurement strength, with the real measurement case exhibiting a smaller entangling phase. Both exhibit exponential scaling of the entanglement near the transition, but they differ in the value of a critical exponent. An intriguing difference between the two cases is that the real measurement case lies at the boundary between two distinct types of critical scaling. On the basis of our results we propose a protocol for realizing a measurement phase transition experimentally via an expansion process.