*Article* **Study on Non-Commutativity Measure of Quantum Discord**

### **Jin Liang \* and Chengwei Zhang**

School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai 200240, China; zcw-i0@sjtu.edu.cn **\*** Correspondence: jinliang@sjtu.edu.cn

Received: 2 May 2019; Accepted: 11 June 2019; Published: 14 June 2019

**Abstract:** In this paper, we are concerned with the non-commutativity measure of quantum discord. We first present an explicit expression of the non-commutativity measure of quantum discord in the two-qubit case. Then we compare the geometric quantum discords for two dynamic models with their non-commutativity measure of quantum discords. Furthermore, we show that the results conducted by the non-commutativity measure of quantum discord are different from those conducted by both or one of the Hilbert-Schmidt distance discord and trace distance discord. These intrinsic differences indicate that the non-commutativity measure of quantum discord is incompatible with at least one of the well-known geometric quantum discords in the quantitative and qualitative representation of quantum correlations.

**Keywords:** quantum discord; non-commutativity measure; dynamic models
