Complete optimal convex approximations of qubit states under $$B_2$$ B 2 distance
Xiao-Bin Liang, Bo Li, Biao‐Liang Ye, Shao-Ming Fei, Xianqing Li‐Jost · Quantum Information Processing · 2018
We consider the optimal approximation of arbitrary qubit states with respect to an available states consisting the eigenstates of two of three Pauli matrices, the $$B_2$$ -distance of an arbitrary target state. Both the analytical formulae of the $$B_2$$ -distance and the corresponding complete optimal decompositions are obtained. The trade-off relations for both the sum and the squared sum of the $$B_2$$ -distances have been analytically and numerically investigated.