I see that conditional $L_2$ distances from uniform are defined in the following way: $L_2(\rho_{AB}\vert \sigma_B)= \text{tr}\left(((\rho_{AB}- \mu_{A} \otimes \rho_{B}) (\mathbb{I}_A \otimes \sigma_B^{-1/2}))^2\right)$ where $\mu_{A}$ is the maximally mixed state on $A$. I do not understand motivation for this definition.Furthermore, conditional collision entropy is defined in the follwing way: $S_2(\rho_{AB} \vert \sigma_B)= - \log(L_2(\rho_{AB}\vert \sigma_B))$. Is there an $L_p$ analogue of this?
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