Proposed Beamsplitter Network for Heralded 4-ion W-state Remote Entanglement

The number of families of entanglement, such as Bell, W, and GHZ states, grows as the number of entangled qubits increases. These families of entanglement cannot be transformed into another using only local operations and classical communication, and many families of entanglement have different useful properties. For example, W-states maximize residual entanglement under qubit loss. Ion based qubits may be entangled by simultaneously sending a photon emitted from each qubit through a shared interferometer. The design of the interferometer must be chosen to produce and herald successful entanglement. Here we show beamsplitter networks can be used to herald 3- and 4-qubit GHZ- and W-states via 3- and 4-photon coincident detection without the use of other ancilla qubits. Though slower than other proposed methods, as the speed and size of quantum networks grows, the interferometers shown could enhance connectivity without requiring operations at intermediate nodes. Distribution Statement A. Approved for public release: distribution unlimited. Case number AFRL-2021-0178.