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Feynman's sum-over-histories formulation of quantum mechanics has beenconsidered a useful calculational tool in which virtual Feynman historiesentering into a coherent quantum superposition cannot be individually measured.Here we show that sequential weak values, inferred by consecutive weakmeasurements of projectors, allow direct experimental probing of individualvirtual Feynman histories thereby revealing the exact nature of quantuminterference of coherently superposed histories. Because the total sum ofsequential weak values of multi-time projection operators for a complete set oforthogonal quantum histories is unity, complete sets of weak values could beinterpreted in agreement with the standard quantum mechanical picture. We alsoelucidate the relationship between sequential weak values of quantum historieswith different coarse-graining in time and establish the incompatibility ofweak values for non-orthogonal quantum histories in history Hilbert space.Bridging theory and experiment, the presented results may enhance ourunderstanding of both weak values and quantum histories.

Probing finite coarse-grained virtual Feynman histories with sequential weak values