Optimal convex approximations of quantum states
Massimiliano Federico Sacchi · Physical Review A · 2017
We consider the problem of optimally approximating an unavailable quantum state $\ensuremath{\rho}$ by the convex mixing of states drawn from a set of available states ${{\ensuremath{ u}}_{i}}$. The problem is recast to look for the least distinguishable state from $\ensuremath{\rho}$ among the convex set ${\ensuremath{\sum}}_{i}{p}_{i}{\ensuremath{ u}}_{i}$, and the corresponding optimal weights ${{p}_{i}}$ provide the optimal convex mixing. We present the complete solution for the optimal convex approximation of a qubit mixed state when the set of available states comprises the three bases of the Pauli matrices.