Renormalization of quantum coherence and quantum phase transition in the Ising model

Abstract

Quantifying quantum coherence of a given system not only plays an important role in quantum information science but also promotes our understanding of some basic problems, such as quantum phase transition. Conventional quantum coherence measures, such as l1-norm of coherence and relative entropy of coherence, are widely used to study quantum phase transition. Here we adopt a basis-independent coherence measure that is a quantum version of the Jensen–Shannon divergence to investigate the property of total quantum coherence, as well as its two contributions in quantum critical systems. Based on the quantum renormalization group method, we propose an analysis of the distribution of quantum coherence in the Ising system near the quantum critical point. We directly obtain the tradeoff relation, singular property, and scaling behavior in the Ising system. Furthermore, the monogamy relation is also studied in detail. These results further expand our understanding of quantum coherence as well as to enlarge the applications in using quantum coherence to reflect quantum critical phenomena.