  We generalize the scattering theory of quantum shot noise to include the full
spin-density matrix of electrons injected from a spin-filtering or
ferromagnetic electrode into a quantum-coherent nanostructure governed by
various spin-dependent interactions. This formalism yields the spin-resolved
shot noise power for different experimental measurement setups--with
ferromagnetic source and ferromagnetic or normal drain electrodes--whose
evaluation for the diffusive multichannel quantum wires with the Rashba (SO)
spin-orbit coupling shows how spin decoherence and dephasing lead to
substantial enhancement of charge current fluctuations (characterized by Fano
factors $> 1/3$). However, these processes and the corresponding shot noise
increase are suppressed in narrow wires, so that charge transport experiments
measuring the Fano factor $F_{\uparrow \to \uparrow \downarrow}$ in a
ferromagnet/SO-coupled-wire/paramagnet setup also quantify the degree of
phase-coherence of transported spin--we predict a one-to-one correspondence
between the magnitude of the spin polarization vector and $F_{\uparrow \to
\uparrow \downarrow}$.
