Fig. 2: Generation and verification of genuine multidimensional multiphoton entanglement in the graph-based quantum device.
a–e, By reconfiguring the sublattice and accordingly the graph’s topologies, it allows on-chip generation, manipulation, analysis and verification of different multidimensional multiphoton entanglement structures. For each state, it shows the graph topology with a superposition of perfect matchings, and the corresponding two-dimensional lattice (depicted for simplicity, but exactly implemented in the VLSI device) with a certain configuration of connectivity of nonlinear sources (yellow squares) and single-photon pathways (red lines). The encoding of a logical basis is indicated on the sources. The photon pathways are labelled by {A, B, C, D}. The entangled states are represented by concentric circles connected by green lines, where the circles represent photonic qudits and the number of circles implies their local dimension; the lines represent entanglement between the photonic qudits. Here n denotes the number of photons and d denotes the local dimensionality. The norm values of the reconstructed density matrices (∣ρ∣) and measured quantum-state fidelities (F) are shown for the below states: four-photon three-dimensional \({\left\vert {{{\rm{GHZ}}}}\right\rangle }_{3}^{4}\) state, F = 0.722(18) > 2/3 (a); four-photon two-dimensional \({\left\vert {{{\rm{GHZ}}}}\right\rangle }_{2}^{4}\) state, F = 0.792(12) > 1/2 (b); two-photon three-dimensional \({\left\vert {{{\rm{GHZ}}}}\right\rangle }_{3}^{2}\) (Bell) state, F = 0.966(2) (c); three-photon |W〉3 state, F = 0.729(19) > 1/2 (d); tracing out one part of |W〉3 and the remaining part retains the entanglement (e). Partial density matrices are reconstructed by measuring dn diagonal elements (in the computational basis) and d off-diagonal elements (in the coherent basis) coloured in blue in all the plots, whereas the remaining elements in yellow are not measured. In c, the complete quantum-state tomography is implemented instead. The values in the parentheses denote the ±1σ uncertainty, estimated by Monte Carlo methods considering Poissonian photon statistics.
