Quantum Optimal Convex Approximation Test Standard Based on Conherence Measure
The optimal convex approximation of quantum states has a broad prospect in the field of quantum information and quantum technology,mainly by using suitable state distance measurement method,and by proba-bility convex mixing of a series of given quantum states,search for the most indistinguishable quantum state from the target quantum state.The common methods of distance measurement are trace distance,l1-norm,fidelity and so on.Here,we propose an optimal criterion based on coherence measure to test the practical application of quantum optimal convex approximation,by comparing the effects of trace distance,l1-norm,and fidelity in cal-culating the optimal approximation problem of Pauli distance,we find that the optimal convex approximation co-herence based on fidelity distance measure is the best.In addition,we generalize the range of a given quantum state to any quantum state,solve the analytical expression when the optimal convex approximation reaches the maximum coherence,and study its corresponding physical mechanism.