  We show that the complete photoemission dynamics in situations of
electron-ion entanglement can be retrieved from photoelectron spectral
measurements without information on the ion. To this end, we develop an
energy-time analysis of the photoelectron's reduced density matrix based on
first principles. We test and assess our approach with numerical simulations on
a low dimensional model molecule in interaction with broadband composite pulses
occulting the vibrational resolution. Our method is directly applicable to
recent experimental schemes measuring the photoelectron reduced density
matrices in atomic and molecular photoemission. Therefore, it opens a new
window on the dynamics of decoherence and entanglement at the attosecond
timescale.
