  By viewing current in the detecting lead of a spintronic device as being an
ensemble of flowing spins corresponding to a mixed quantum state, where each
spin itself is generally described by an improper mixture generated during the
transport where it couples to other degrees of freedom due to spin-orbit (SO)
interactions or inhomogeneous magnetic fields, we introduce the spin density
operator associated with such current expressed in terms of the spin-resolved
Landauer transmission matrix of the device. This formalism, which provides
complete description of coupled spin-charge quantum transport in open
finite-size systems attached to external probes, is employed to understand how
initially injected pure spin states, comprising fully spin-polarized current,
evolve into the mixed ones corresponding to partially polarized current. We
analyze particular routes that diminish spin coherence (signified by decay of
the off-diagonal elements of the current spin density matrix) in
two-dimensional electron gas-based devices due to the interplay of the Rashba
and/or Dresselhaus SO coupling and: (i) scattering at the boundaries or
lead-wire interface in ballistic semiconductor nanowires; or (ii)
spin-independent scattering off static impurities in both weakly and strongly
localized disordered nanowires. The physical interpretation of spin decoherence
in the course of multichannel quantum transport in terms of the entanglement of
spin to an effectively zero-temperature ``environment'' composed of more than
one open orbital conducting channels offers insight into some of the key
challenges for spintronics: controlling decoherence of transported spins and
emergence of partially coherent spin states in all-electrical spin manipulation
schemes based on the SO interactions in realistic semiconductor structures.
