  Attosecond streaking of atomic photoemission holds the promise to provide
unprecedented information on the release time of the photoelectron. We show
that attosecond streaking phase shifts indeed contain timing (or spectral
phase) information associated with the Eisenbud-Wigner-Smith time delay matrix
of quantum scattering. However, this is only accessible if the influence of the
streaking infrared (IR) field on the emission process is properly accounted
for. The IR probe field can strongly modify the observed streaking phase shift.
We show that the part of the phase shift ("time shift") due to the interaction
between the outgoing electron and the combined Coulomb and IR laser fields can
be described classically. By contrast, the strong initial-state dependence of
the streaking phase shift is only revealed through the solution of the
time-dependent Schr\"odinger equation in its full dimensionality. We find a
time delay between the hydrogenic 2s and 2p initial states in He+ exceeding
20as for a wide range of IR intensities and XUV energies.
