Experimental implementation of Hardy-like quantum pigeonhole paradoxes

We present the general Hardy-like quantum pigeonhole paradoxes for \textit{n}-particle states, and find that each of such can be simply associated to an un-colorable solution a specific vertex-coloring problem induced from projected-coloring graph (a kind unconventional graph). Besides, as special Hardy's paradox, several kinds even give rise higher success probability in demonstrating conflict between mechanics local or noncontextual realism than previous paradoxes. Moreover, not only multi-qubit but high-dimensional states exhibit In contrast one type contradiction presented original two three-qubit minimal illustration are discussed our work, optical experiment verify stronger paradox is performed. This provides innovative thoughts methods exploring new types multi-party nonlocality may have potential applications untrusted communications device-independent random number generation.