  The inverse problem of electrical impedance tomography is severely ill-posed.
In particular, the resolution of images produced by impedance tomography
deteriorates as the distance from the measurement boundary increases. Such
depth dependence can be quantified by the concept of distinguishability of
inclusions. This paper considers the distinguishability of perfectly conducting
ball inclusions inside a unit ball domain, extending and improving known
two-dimensional results to an arbitrary dimension $d \geq 2$ with the help of
Kelvin transformations. The obtained depth-dependent distinguishability bounds
are also proven to be optimal.
