Complete Optimal Convex Approximations of Qubit States under B₂ Distance

Xiao-Bin Liang, Bo Li, Biao-Liang Ye, Shao-Ming Fei, and Xianqing Li-Jost

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Submission date: 20. Aug. 2018
Pages: 10
published in: Quantum information processing, 17 (2018) 7, art-no. 185 
DOI number (of the published article): 10.1007/s11128-018-1948-0
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Abstract:
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 B₂-distance of an arbitrary target state. Both the analytical formulae of the B₂-distance and the corresponding complete optimal decompositions are obtained. The tradeoff relations for both the sum and the squared sum of the B₂-distances have been analytically and numerically investigated.