Phase transitions in sequential weak measurements

TL;DR

This paper reveals that phase transitions occur in sequential quantum measurements, with measurement result distributions analogous to classical lattice spin models, providing new insights into quantum measurement processes.

Contribution

It demonstrates the occurrence of phase transitions in sequential quantum measurements and maps measurement distributions to classical spin models, a novel connection.

Findings

Measurement results follow a Boltzmann distribution similar to classical spin models.

A transition from weak to strong measurements corresponds to a phase transition in the spin model.

Sequential measurements can produce a projective measurement at critical points.

Abstract

Quantum measurements and phase transitions are seemingly uncorrelated topics, but here we show that phase transitions occur in sequential quantum measurements. We find that the probability distribution of the measurement results of a sequence of quantum measurements on a two-level system (e.g. a qubit) is equivalent to the Boltzmann distribution of a classical lattice spin model. So the measurement results present phase transitions similar to those in the lattice spin model. In sequential commuting positive-operator valued measurements, the probability distribution is mapped to a long-range Ising model in the weak-measurement regime, and a projective measurement emerges from a sequence of weak measurement when the strength or the number of measurements becomes above certain critical values, which correspond to a second-order ferromagnetic phase transition of the lattice spin model. These findings not only provide new insights on sequential quantum measurements, but may also have potential applications in quantum technologies.