Fig. 2: Experimentally generating and manipulating the six-photon graph state.

a On the left is the linear optical circuit for generating the target graph state on the right. Three photon-pair sources are represented as black boxes with each horizontal line representing a labelled optical mode containing one photon. Two sources produce Bell states, \(\left\vert {\Phi }^{+}\right\rangle\), while the third generates a biseparable state with each photon in \(\left\vert +\right\rangle\). The two-qubit fusion gates are denoted by two squares on the modes they act upon connected by a vertical line. Single-qubit operations, i.e., Hadamard and Pauli-Z gates are shown as squares with letters \({\mathbb{H}}\) and Z respectively. b The set of graph transformations for obtaining the four-qubit GHZ state, in modes {1, 2, 5, 6}, are depicted in the red path. This corresponds to local operations consisting of single-qubit gates \({{{\rm{N}}}}\doteq \sqrt{-i{{{\rm{X}}}}}\) and \({{{\rm{T}}}}\doteq \sqrt{i{{{\rm{Z}}}}}\), where X and Z are again Pauli gates, followed by quantum measurements on non-participatory qubits {3, 4} in the Z basis. The remaining qubits can be measured in the joint-Z or-X basis allowing us to evaluate the key rate performance for the NQKD method. c Local graph operations for obtaining Bell pairs between nodes {1, 2} and {5, 6} (top) and a Bell pair between nodes {5, 6} (bottom) which are needed for the 2QKD approach.