A multi-photon state behaves like a stochastic mixture of distinguishability patterns exactly when its interference parameters depend only on permutation cycle structure, enabling a compact partition representation and error mitigation.
Sampling of partially distinguishable bosons and the relation to the multidimensional permanent
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The collective interference of partially distinguishable bosons in multi-mode networks is studied via double-sided Feynman diagrams. The probability for many-body scattering events becomes a multi-dimensional tensor-permanent, which interpolates between distinguishable particles and identical bosons, and easily extends to mixed initial states. The permanent of the distinguishability matrix, composed of all mutual scalar products of the single-particle mode-functions, emerges as a natural measure for the degree of interference: It yields a bound on the difference between event probabilities for partially distinguishable bosons and the idealized species, and exactly quantifies the degree of bosonic bunching.
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Incoherent behavior of partially distinguishable photons
A multi-photon state behaves like a stochastic mixture of distinguishability patterns exactly when its interference parameters depend only on permutation cycle structure, enabling a compact partition representation and error mitigation.