Measurement-Induced Spectral Transition

TL;DR

This paper investigates a spectral transition in noisy quantum systems under weak measurements, linking spectral properties to entanglement scaling and memory loss timescales, revealing a novel phase transition analogy.

Contribution

It introduces the concept of a spectral transition in quantum dynamics and connects it to entanglement phases and memory loss, providing new insights into quantum measurement effects.

Findings

Spectral gap correlates with entanglement entropy scaling.

Transition from volume-law to area-law entanglement phases.

Spectral transition affects the timescale of memory loss.

Abstract

We show that noisy quantum dynamics exposed to weak measurements exhibit a spectral transition between gapless and gapped phases. To this end, we employ the Lyapunov spectrum obtained through singular values of a non-unitary matrix describing the dynamics. We discover that the gapless and gapped phases respectively correspond to the volume-law and area-law phases of the entanglement entropy for the dominant Lyapunov vector. This correspondence between the spectral gap and the scaling of entanglement offers an intriguing analogy with ground-state phase transitions. We also discuss some crucial differences from ground-state transitions, such as the scaling law of the entanglement and the exponentially small gaps. Furthermore, we show that the spectral transition leads to the transition of the timescale for the memory loss of initial states.