Production and detection of three-qubit entanglement in the Fermi sea

TL;DR

This paper demonstrates a method to generate and detect three-qubit entanglement in the Fermi sea using quantum Hall edge channels, without electron-electron interactions, and characterizes it via noise measurements.

Contribution

It introduces a novel scheme for creating three-qubit entanglement in electronic systems without interactions, using edge channels and tunneling contacts, and provides a way to measure entanglement through noise.

Findings

Maximally entangled GHZ state achieved with channel-independent tunneling.

Low-frequency noise measurements can bound the entanglement (tangle).

Entanglement persists even in thermal equilibrium sources.

Abstract

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.