  We propose a qubit-environment entanglement measure which is tailored for
evolutions that lead to pure dephasing of the qubit, such as are abundant in
solid state scenarios. The measure can be calculated directly form the density
matrix without minimization of any kind. In fact it does not require the
knowledge of the full density matrix, and it is enough to know the initial
qubit state and the states of the environment conditional on qubit pointer
states. This yields a computational advantage over standard entanglement
measures, which becomes large when there are no correlations between
environmental components in the conditional environmental states. In contrast
to all other measures of mixed state entanglement, the measure has a
straightforward physical interpretation directly linking the amount of
information about the qubit state which is contained in the environment to the
amount of qubit-environmnent entanglement. This allows for a direct extension
of the pure state interpretation of entanglement generated during pure
dephasing to mixed states, even though pure-state conclusions about qubit
decoherence are not transferable.
