Comment on “Optimal convex approximations of quantum states”

In a recent paper, M. F. Sacchi [Phys. Rev. A 96, 042325 (2017)] addressed the general problem of approximating an unavailable quantum state by the convex mixing of different available states. For the case of qubit mixed states, we show that the analytical solutions in some cases are invalid. In this Comment, we present complete analytical solutions for the optimal convex approximation. Our solutions can be viewed as correcting and supplementing the results in the aforementioned paper.

Figure 1

Plot of $D_{B_3}\left(\rho \right)$ as a function of the parameter $\varphi =\frac{\pi }{3}$ from our result.

Figure 2

Difference in $D_{B_3}\left(\rho \right)$ between our result and that of Ref. [1], as a function of the phase parameter $\varphi =\frac{\pi }{3}$.