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Quantum superposition of high-dimensional states enables both computationalspeed-up and security in cryptographic protocols. However, the exponentialcomplexity of tomographic processes makes certification of these properties achallenging task. In this work, we experimentally certify coherence witnessestailored for quantum systems of increasing dimension, using pairwise overlapmeasurements enabled by a six-mode universal photonic processor fabricated witha femtosecond laser writing technology. In particular, we show theeffectiveness of the proposed coherence and dimension witnesses for qudits ofdimensions up to 5. We also demonstrate advantage in a quantum interrogationtask, and show it is fueled by quantum contextuality. Our experimental resultstestify to the efficiency of this novel approach for the certification ofquantum properties in programmable integrated photonic platforms

Experimental certification of contextuality, coherence and dimension in a programmable universal photonic processor