Distinguishability in quantum interference with the squeezed states

Valery Shchesnovich

doi:10.1103/PhysRevA.105.063703

paper

Distinguishability in quantum interference with the squeezed states

arXiv:2109.01857 · doi:10.1103/PhysRevA.105.063703

Abstract

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

arXiv comment21 pages, 2 figures; In the last revision: Subsection IIA is added with mathematical details of the approach used. Typo in Eq. (62) is corrected. New Eqs. (21), (23) (24) and (47) are added. DOI added

Distinguishability in quantum interference with the squeezed states

Abstract

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