Density matrices and entropies

Ingemar Bengtsson, Karol Życzkowski

Anna Jenčová

Mary Beth Ruskai

Yuan-Feng Song, Li-Zhu Ge, Yaokun Wang +2 more

Abstract In this paper, we calculate the density matrices of one class of X states in the three-dimensional mutually unbiased bases and find that the density matrices are equal to their corresponding conjugate transpose matrices. After obtaining the relations of these density matrices, we calculate the relative entropies of coherence for the density matrices of X states in these nontrivial mutually unbiased bases and obtain that their relative entropies of coherence are equal. At last, the density matrices of other two classes of X states in these mutually unbiased bases are discussed. We also investigate their relative entropies of coherence and clarify their relationships.

Kevin Vanslette

We find that the standard relative entropy and the Umegaki entropy are designed for the purpose of inferentially updating probabilities and density matrices, respectively. From the same set of inferentially guided design criteria, both of the previously stated entropies are derived in parallel. This formulates a quantum maximum entropy method for the purpose of inferring density matrices in the absence of complete information.

Péter R. Śurján