  Building on a previous proposal for the entanglement of electron-hole pairs
in the Fermi sea, we show how 3 qubits can be entangled without using
electron-electron interactions. As in the 2-qubit case, this electronic scheme
works even if the sources are in (local) thermal equilibrium -- in contrast to
the photonic analogue. The 3 qubits are represented by 4 edge-channel
excitations in the quantum Hall effect (2 hole excitations plus 2 electron
excitations with identical channel index). The entangler consists of an
adiabatic point contact flanked by a pair of tunneling point contacts. The
irreducible 3-qubit entanglement is characterized by the tangle, which is
expressed in terms of the transmission matrices of the tunneling point
contacts. The maximally entangled Greenberger-Horne-Zeilinger (GHZ) state is
obtained for channel-independent tunnel probabilities. We show how
low-frequency noise measurements can be used to determine an upper and lower
bound to the tangle. The bounds become tighter the closer the electron-hole
state is to the GHZ state.
