  A bosonic state is commonly considered nonclassical (or quantum) if its
Glauber-Sudarshan $P$ function is not a classical probability density, which
implies that only coherent states and their statistical mixtures are classical.
We quantify the nonclassicality of a single qubit, defined by the vacuum and
single-photon states, by applying the following four well-known measures of
nonclassicality: (1) the nonclassical depth, $\tau$, related to the minimal
amount of Gaussian noise which changes a nonpositive $P$ function into a
positive one; (2) the nonclassical distance $D$, defined as the Bures distance
of a given state to the closest classical state, which is the vacuum for the
single-qubit Hilbert space; together with (3) the negativity potential (NP) and
(4) concurrence potential, which are the nonclassicality measures corresponding
to the entanglement measures (i.e., the negativity and concurrence,
respectively) for the state generated by mixing a single-qubit state with the
vacuum on a balanced beam splitter. We show that complete statistical mixtures
of the vacuum and single-photon states are the most nonclassical single-qubit
states regarding the distance $D$ for a fixed value of both the depth $\tau$
and NP in the whole range $[0,1]$ of their values, as well as the NP for a
given value of $\tau$ such that $\tau>0.3154$. Conversely, pure states are the
most nonclassical single-qubit states with respect to $\tau$ for a given $D$,
NP versus $D$, and $\tau$ versus NP. We also show the "relativity" of these
nonclassicality measures by comparing pairs of single-qubit states: if a state
is less nonclassical than another state according to some measure then it might
be more nonclassical according to another measure. Moreover, we find that the
concurrence potential is equal to the nonclassical distance for single-qubit
states.
