  We investigate a separability criterion based on the computable cross-norm
(CCNR), and a related quantity called the CCNR negativity. We introduce a
reflected version of the CCNR negativity, and discuss its connection with other
well-established entanglement-related quantities, namely the reflected entropy
and the operator entanglement entropy. For free fermionic and bosonic theories,
we derive exact formulas in terms of two-point correlation functions, which
allow for systematic numerical investigations and, in principle, analytical
treatments. For systems with a global $U(1)$ symmetry, we study the
symmetry-resolved reflected entropy and CCNR negativity. We provide conformal
field theory (CFT) results for the charged moments in the case of adjacent
intervals, finding perfect agreement with the numerics. We observe an
equipartition of reflected entropies and CCNR negativities, both for
free-fermions and free-boson models. The first charge-dependent corrections are
conjectured for fermions, and worked out from the CFT calculations for bosons.
