A unique_ptr must always store its deleter. Now, if the deleter is a class type with no state, then the unique_ptr can make use of empty base optimization so that the deleter does not use any additional space.
How exactly this is done differs between implementations. For instance, both libc++ and MSVC store the managed pointer and the deleter in a compressed pair, which automatically gets you empty base optimization if one of the types involved is an empty class.
From the libc++ link above
template <class _Tp, class _Dp = default_delete<_Tp> >
class _LIBCPP_TYPE_VIS_ONLY unique_ptr
{
public:
typedef _Tp element_type;
typedef _Dp deleter_type;
typedef typename __pointer_type<_Tp, deleter_type>::type pointer;
private:
__compressed_pair<pointer, deleter_type> __ptr_;
libstdc++ stores the two in an std::tuple and some Google searching suggests their tuple implementation employs empty base optimization but I can’t find any documentation stating so explicitly.
In any case, this example demonstrates that both libc++ and libstdc++ use EBO to reduce the size of a unique_ptr with an empty deleter.