  The quantum world distinguishes itself from the classical world by being
governed by probability amplitudes rather than probabilities. On a
single-particle level, quantum phases can be manipulated leading to observable
interference patterns that can be used as a probe e.g. in matter wave
microscopy. But the quantum world bears even more fascinating effects when it
comes to the interplay between more than one particle. Correlations between
quantum particles such as entanglement can be exploited to speed up
computational algorithms or enable secure cryptography. Here, we propose and
numerically explore a thought experiment to address the question whether
quantum correlations between particles can be used in matter wave microscopy.
Specifically, we address the following questions: How can information be
transferred between two mutually spin-correlated free-electron wavepackets? Can
Coulomb and exchange correlations be linked to the decoherence mechanism of
matter waves? Using a time-dependent Hartree-Fock algorithm, we will show that
the exchange term has a substantial role in transferring the information
between two mutually spin-correlated electrons, whereas the Hartree potential
(or mean-field Coulomb potential) dominates the dephasing on a single-particle
level. Our findings might facilitate fermionic matter-wave interferometry
experiments in which it is possible to retrieve information about non-classical
correlations and the mechanism of decoherence in open versus closed quantum
systems.
