Efficient detection of localization transitions using predictability

TL;DR

This paper introduces predictability as an efficient and robust marker for detecting localization transitions in quantum systems, requiring fewer measurements than traditional coherence or entanglement methods.

Contribution

It demonstrates that local predictability can effectively identify localization transitions, offering a practical and resource-efficient alternative to existing quantum coherence-based detection techniques.

Findings

Predictability reliably indicates localization transitions.

Predictability requires exponentially fewer measurements than coherence or entanglement.

The method is experimentally feasible for probing quantum phase transitions.

Abstract

Identifying phase transition points is a fundamental challenge in condensed matter physics, particularly for transitions driven by quantum interference effects, such as Anderson and many-body localization. Recent studies have demonstrated that quantum coherence provides an effective means of detecting localization transitions, offering a practical alternative to full quantum state tomography and related approaches. Building on this idea, we investigate localization transitions through complementarity relations that connect local predictability, local coherence, and entanglement in bipartite pure states. Our results show that predictability serves as a robust and efficient marker for localization transitions. Crucially, its experimental determination requires exponentially fewer measurements than coherence or entanglement, making it a powerful tool for probing quantum phase transitions.