Abstract
Utilizing the l1 norm as the quantum state distance metric, we consider the Pauli distance of arbitrary target quantum states, that is, the optimal convex approximation of any qubit mixed states relative to the available state of pairs of eigenstates in three Pauli matrices. We get the complete analytical expressions for B1 -distance, B2 -distance and B3 -distance. We determine the parameter range for the optimal approximation of each B2 -distance in eight distinct scenarios. Furthermore, some trade-off relations about B2 -distances are also studied.
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