Distinguishability in quantum interference with multimode squeezed states

Distinguishability theory is developed for quantum interference of the squeezed vacuum states on unitary linear interferometers. It found that entanglement photon pairs over Schmidt modes one sources distinguishability. The distinguishability quantified by symmetric part internal state $n$ photons, whose normalization $q_{2n}$ probability $2n$ photons interfere as indistinguishable. For two $q_{4}=(1+ 2\mathbb{P} )/3$, where $\mathbb{P} $ purity ($K=1/\mathbb{P} number). a fixed $\mathbb{P}$, decreases exponentially fast in $n$. example, experimental Gaussian boson sampling H.-S.~Zhong \textit{et al} [Science \textbf{370}, 1460 (2020)], achieved $\mathbb{P}\approx 0.938$ average number $2n\ge 43$ gives $q_{2n}\lesssim 0.5$, i.e., close to middle line between indistinguishable and distinguishable photons. In derivation all results first-order quantization representation based particle decomposition Hilbert space identical bosons serves an indispensable tool. approach can be applied also generalized (non-Gaussian) states, such those recently generated three-photon parametric down-conversion.