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We propose a qubit-environment entanglement measure which is tailored forevolutions that lead to pure dephasing of the qubit, such as are abundant insolid state scenarios. The measure can be calculated directly form the densitymatrix without minimization of any kind. In fact it does not require theknowledge of the full density matrix, and it is enough to know the initialqubit state and the states of the environment conditional on qubit pointerstates. This yields a computational advantage over standard entanglementmeasures, which becomes large when there are no correlations betweenenvironmental components in the conditional environmental states. In contrastto all other measures of mixed state entanglement, the measure has astraightforward physical interpretation directly linking the amount ofinformation about the qubit state which is contained in the environment to theamount of qubit-environmnent entanglement. This allows for a direct extensionof the pure state interpretation of entanglement generated during puredephasing to mixed states, even though pure-state conclusions about qubitdecoherence are not transferable.

A measure of qubit environment entanglement for pure dephasing evolutions