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The current shift in the quantum optics community towards experiments with many modes and photons necessitates new classical simulation techniques that efficiently encode many-body quantum correlations and go beyond the usual phase-space formulation. To address this pressing demand we formulate linear quantum optics in the language of tensor network states. We extensively analyze the quantum and classical correlations of time-bin interference in a single fiber loop. We then generalize our results to more complex time-bin quantum setups and identify different classes of architectures for high-complexity and low-overhead boson sampling experiments.

We introduce a method for the verification of nonclassical light which is independent of the complex interaction between the generated light and the material of the detectors. This is accomplished by means of a multiplexing arrangement. Its theoretical description yields that the coincidence statistics of this measurement layout is a mixture of multinomial distributions for any classical light field and any type of detector. This allows us to formulate bounds on the statistical properties of classical states. We apply our directly accessible method to heralded multiphoton states which are detected with a single multiplexing step only and two detectors, which are in our work superconducting transition-edge sensors. The nonclassicality of the generated light is verified and characterized through the violation of the classical bounds without the need for characterizing the used detectors., Comment: close to published version

Spatial quantum correlations are an important resource for quantum imaging and future quantum technologies based on high-dimensional entanglement. We experimentally explore spatial correlations in four-photon states generated by a highly efficient parametric down-conversion process in a 2 mm long periodically poled KTP crystal. The four-photon states produced in the crystal contain a contribution due to independent double pairs produced via spontaneous pair emission and a highly correlated four-photon state produced by stimulated emission of a second photon pair. We separate this contribution and introduce a joint spatial density for stimulated pair emission. We observe a maximum visibility $\ensuremath{\chi}=0.25$ of the four-photon state for a 1.5 nm bandpass filter.

This paper demonstrates the engineering of spatially entangled two-photon states behind a double slit by tailoring the incident pure two-photon state. We experimentally characterize many different two-photon states by measuring their complete two-photon interference patterns in the far field of the double slit. Spatial entanglement right behind the double slit can reside in either the modulus or the phase of the two-photon field. The balance between these two types of entanglement is fully controlled by experimentally utilizing the phase-front curvatures of the pump beam and the phase-matching profile. We project either a far-field image or a magnified near-field image of the two-photon source onto the double slit. Our theoretical analysis shows how the two-photon interference pattern behind the double slit effectively acts as a phase-sensitive probe of the incident two-photon field profile. We thus present phase-sensitive measurements of the generated two-photon field profile probed in an image plane of the two-photon source.