Trade-off relations between quantum coherence and measure of many-body localization

TL;DR

This paper establishes exact trade-off relations between quantum coherence measures and localization indicators like IPR, revealing how coherence characterizes many-body localization transitions in disordered quantum systems.

Contribution

It proves new complementarity and trade-off relations between quantum coherence and IPR, linking coherence to many-body localization diagnostics.

Findings

Quantum coherence measures satisfy trade-off relations with IPR.

Coherence can characterize the delocalization to localization transition.

Relations provide insights into bipartite entanglement across MBL transition.

Abstract

Quantum coherence, a fundamental resource in quantum computing and quantum information, often competes with localization effects that affects quantum states in disordered systems. In this work, we prove exact trade-off relations between quantum coherence and a measure of localization and many-body localization, namely, the inverse participation ratio (IPR). We prove that for a pure quantum state, $l_1$-norm of quantum coherence and the relative entropy of coherence satisfy complementarity relations with IPR. For a mixed state, IPR and the $l_2$-norm of quantum coherence as well as relative entropy of coherence satisfy trade-off inequalities. These relations suggest that quantum coherence, in disordered quantum systems is also an ideal characterization of the delocalisation to many-body localisation transition, much like IPR, which is a well-known diagnostic of MBL. These relations also provide insight into the unusual properties of bipartite entanglement entropy across the MBL transition. We believe that these trade-off relations can help in better understanding of how coherence can be preserved or lost in realistic many-body quantum systems, which is vital for developing robust quantum technologies and uncovering new phases of quantum matter.