TTMS30. Metrics induced by certain fidelities
Speaker: Dr. Minh-Toan Ho, Hanoi Institute of Mathematics, Vietnam
Abstract: Motivated by measuring the degree of similarity of a pair of quantum states (density matrices), we consider the metric property of the modified Bures angles and modified Bures distances of symmetric functions which are extensions of some fidelity measures on the quantum state space and give answers to the questions written the work by Liang etc. [Y. C. Liang, Y. H. Yeh, P. E. M. F. Mendon, R. Y. Teh, M. D. R. and P. D. Drummond, Quantum fidelity measures for mixed states, Rep. Prog. Phys. 82(7) (2019), 076001] . We also consider this problem on the space P of nonzero positive semi-definite matrices. We use the positive semi-definiteness of the Gram-type matrices to characterize the metric property of the modified Bures angles. As a consequence, we can show that the modified Bures angles induced by the geometric mean, harmonic mean, minimum and maximum of two positive numbers are metrics on P.