Creating a Remote GHZ State in a Trapped Ion Quantum Network

Greenberger-Horne-Zeilinger (GHZ) states are a cornerstone of quantum information processing, enabling advancements in quantum computing, communication, and metrology. In this work, we demonstrate the creation of a three-qubit maximally-entangled GHZ state between physically-separated trapped ion qubit nodes via three-photon interference. We generate the photonic qubits by exciting $^{138}$Ba$^+$ ground-state Zeeman qubits and using the spontaneously emitted 493 nm photon's polarization degree-of-freedom. 

After collection, we interfere the photons through a circuit of polarizing beam-splitters and detect coincident three-photon events that herald a maximally-entangled GHZ state in the three trapped ion qubits. With this remotely-entangled GHZ state, we are able to demonstrate Mermin’s inequality in a distributed network, as well as conduct a three-party quantum game. Remotely-entangled GHZ states are powerful tools for quantum metrology, providing lower MSE (mean squared error) than their non-entangled counterparts, and we show progress towards the first distributed realization.