A monochromatic laser pumping a parametric down conversion crystal generates frequency entangled photon pairs. We study this experimentally by addressing such frequency entangled photons at telecommunication wavelengths (around 1550 nm) with fiber optics components such as electrooptic phase modulators and narrow band frequency filters. The theory underlying our approach is developed by introducing the notion of frequency bin entanglement. Our results show that the phase modulators address coherently up to eleven frequency bins, leading to an interference pattern which can violate a Bell inequality adapted to our setup by more than five standard deviations.

We report the experimental generation of polarization-entangled photons at telecommunication wavelengths using spontaneous four-wave mixing in silicon-on-insulator wire waveguides. The key component is a 2D coupler that transforms path entanglement into polarization entanglement at the output of the device. Using quantum state tomography we find that the produced state has fidelity 88% with a pure nonmaximally entangled state. The produced state violates the CHSH Bell inequality by S=2.37 ± 0.19.

Frequency-entangled photons can be readily produced using parametric down-conversion. We have recently shown how such entanglement could be manipulated and measured using electro-optic phase modulators and narrow-band frequency filters, thereby leading to two-photon interference patterns in the frequency domain. Here we introduce new theoretical and experimental developments showing that this method is potentially a competitive platform for the realization of quantum communication protocols in standard telecommunication fibres. We derive a simple theoretical expression for the coincidence probabilities and use it to optimize a Bell inequality. Furthermore, we establish an equivalence between the entangled-photon scheme and a classical interference scheme. Our measurements of two-photon interference in the frequency domain yield raw visibilities in excess of 99%. We use our high-quality setup to experimentally validate the theoretical predictions, and in particular we report a violation of the CH74 inequality by more than 18 standard deviations.

The quantum state ψ is a mathematical object used to determine the outcome probabilities of measurements on physical systems. Its fundamental nature has been the subject of discussions since the origin of the theory: Is it ontic, that is, does it correspond to a real property of the physical system? Or is it epistemic, that is, does it merely represent our knowledge about the system? Recent advances in the foundations of quantum theory show that epistemic models that obey a simple continuity condition are in conflict with quantum theory already at the level of a single system. Here we report an experimental test of continuous epistemic models using high-dimensional attenuated coherent states of light traveling in an optical fiber. Due to nonideal state preparation (of coherent states with imperfectly known phase) and nonideal measurements (arising from losses and inefficient detection), this experiment tests only epistemic models that satisfy additional constraints which we discuss in detail. Our experimental results are in agreement with the predictions of quantum theory and provide constraints on a class of ψ-epistemic models.

Radio-frequency phase modulation of frequency entangled photons leads to a two-photon interference pattern in the frequency domain. In recent experiments, the pattern was measured with narrow-band frequency filters which select photons belonging to a given frequency bin. Here we show how photons can be grouped into even and odd frequencies by using periodic frequency filters called interleavers. In our theoretical analysis we show how this reduces the high-dimensional photon state to an effective two-dimensional state. This is of interest for applications such as quantum cryptography or low-dimensional tests of quantum nonlocality. We then report an experimental realization of this proposal. The observed two-photon interference pattern and violation of the CHSH inequality -the simplest binary-outcome Bell inequality -are in good agreement with the theoretical predictions.