Engineering and studying few-electron states in ballistic conductors is a key step towards understanding entanglement in quantum electronic systems. In this Letter, we introduce the intrinsic two-electron coherence of an electronic source in quantum
Hall edge channels and relate it to two-electron wavefunctions and to current noise in an Hanbury Brown--Twiss interferometer. Inspired by the analogy with photon quantum optics, we propose to measure the intrinsic two-electron coherence of a source using low-frequency current correlation measurements at the output of a Franson interferometer. To illustrate this protocol, we discuss how it can distinguish between a time-bin entangled pure state and a statistical mixture of time shifted electron pairs.
Quantum Hall edge channels at integer filling factor provide a unique test-bench to understand decoherence and relaxation of single electronic excitations in a ballistic quantum conductor. In this Letter, we obtain a full visualization of the decoher
ence scenario of energy (Landau) and time (Levitov) resolved single electron excitations at filling factor $ u=2$. We show that the Landau excitation exhibits a fast relaxation followed by spin-charge separation whereas the Levitov excitation only experiences spin-charge separation. We finally suggest to use Hong-Ou-Mandel type experiments to probe specific signatures of these different scenarios.
