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Critical phenomena involve a structural change in the correlations of itsconstituents. These features can be employed in quantum simulators to assesswhen a criticality occurred in medium-size systems, for which phase transitionsare not captured by standard thermodynamical methods. Here we demonstrate theseconcepts in a photonic quantum simulator: we encode the wavefunction of theground state of a three-spin Ising ring by using a pair of entangled photons.The effect of a simulated magnetic field, leading to a critical modification ofthe correlation within the ring, is analysed by studying two- and three-spinentanglement. In particular, we make a quantitative connection between theviolation of Svetlichny's inequality to the amount of three-tangle andtripartite negativity in our ring.

Experimental linear-optics simulation of the ground state of an interacting quantum spin-ring