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Physical Review Letters

Three-Particle Entanglements from Two Entangled Pairs

Anton Zeilinger, Michael Horne, Harald Weinfurter, Marek Żukowski

Published Apr 21, 1997• 302 citations
Publisher

Abstract

When a single particle from two independent entangled pairs is detected in a manner such that it is impossible to determine from which pair the single particle came, the remaining three particles become entangled in a GHZ state. This procedure can be realized with existing sources of entangled photons and with future sources of entangled atoms.

DOI
10.1103/physrevlett.78.3031

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When a single particle from two independent entangled pairs is detected in a manner such that it is impossible to determine from which pair the single particle came, the remaining three particles become entangled in a GHZ state. This procedure can be realized with existing sources of entangled photons and with future sources of entangled atoms.
The premises of the Einstein-Podolsky-Rosen argument for their claim that quantum mechanics is an incomplete theory are inconsistent when applied to three-particle systems in entangled Greenberger-Horne-Zeilinger states.However, thus far there is no experimental confirmation for existence of such states.We propose a technique to obtain Greenberger-Horne-Zeilinger states which rests upon an observation that when a single particle from two independent entangled pairs is detected in a manner such that it is impossible to determine from which pair the single came, the remaining three particles become entangled.
Building on a previous proposal for the entanglement of electron-hole pairs in the Fermi sea, we show how three qubits can be entangled without using electron-electron interactions. As in the two-qubit case, this electronic scheme works even if the sources are in (local) thermal equilibrium---in contrast to the photonic analog. The three qubits are represented by four edge-channel excitations in the quantum Hall effect (two hole excitations plus two electron excitations with identical channel index). The entangler consists of an adiabatic point contact flanked by a pair of tunneling point contacts. The irreducible three-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.