Distinguishability in quantum interference with the squeezed states

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 $q_{2n}$ is the probability that $2n$ photons interfere as indistinguishable. For two pairs of photons $q_4=(1+2\mathbb{P})/3$, where $\mathbb{P}$ is the purity of the squeezed states ($K=1/\mathbb{P}$ is the Schmidt number). For a fixed purity $\mathbb{P}$, the probability $q_{2n}$ 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 $\mathbb{P}\approx 0.938$ for the average number of photons $2n\ge 43$ gives $q_{2n}\lesssim 0.5$, 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.

21 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

References in corpus (15)

• Quantum computational advantage using photons
• Boson sampling with 20 input photons in 60-mode interferometers at $10^{14}$ state spaces
• Probing multimode squeezing with correlation functions
• Experimental Scattershot Boson Sampling
• Purity of Gaussian states: measurement schemes and time-evolution in noisy channels
• Sampling of partially distinguishable bosons and the relation to the multidimensional permanent
• Partial indistinguishability theory for multi-photon experiments in multiport devices
• Multiboson Correlation Interferometry with arbitrary single-photon pure states
• Experimental Gaussian Boson Sampling
• Photon-number superselection and the entangled coherent-state representation
• Observation of detection-dependent multi-photon coherence times
• Demonstration of Temporal Distinguishability in a Four-Photon State and a Six-Photon State
• Tight bound on trace distance between a realistic device with partially indistinguishable bosons and the ideal Boson Sampling
• Distinguishability theory for time-resolved photodetection and boson sampling
• Describing squeezed-light experiments without squeezed-light states

Cited by in corpus (4)

• Waveguided sources of consistent, single-temporal-mode squeezed light: the good, the bad, and the ugly
• Few-mode squeezing in type-I parametric downconversion by complete group velocity matching
• Isoenergetic model for optical downconversion and error-specific limits of the parametric approximation
• Statistical-noise-enhanced multi-photon interference