In our article [1], we claimed to have given the first example of a facet-defining Bell inequality where a genuine positive-operator-valued (POVM) measure is relevant. Specifically, we claimed that any quantum realization of the maximal quantum violation of the Bell inequality I max 12

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The generation of ultrafast laser pulses and the reconstruction of their electric fields is essential for many applications in modern optics. Quantum optical fields can also be generated on ultrafast time scales, however, the tools and methods available for strong laser pulses are not appropriate for measuring the properties of weak, possibly entangled pulses. Here, we demonstrate a method to reconstruct the joint-spectral amplitude of a two-photon energy-time entangled state from joint measurements of the frequencies and arrival times of the photons, and the correlations between them. Our reconstruction method is based on a modified Gerchberg-Saxton algorithm. Such techniques are essential to measure and control the shape of ultrafast entangled photon pulses.

The self-imaging, or Talbot Effect, that occurs with the propagation of periodically structured waves has enabled several unique applications in optical metrology, image processing, data transmission, and matter-wave interferometry. In this work, we report on the first demonstration of a Talbot Effect with single photons prepared in a lattice of orbital angular momentum (OAM) states. We observe that upon propagation, the wavefronts of the single photons manifest self-imaging whereby the OAM lattice intensity profile is recovered. Furthermore, we show that the intensity at fractional Talbot distances is indicative of a periodic helical phase structure corresponding to a lattice of OAM states. This phenomenon is a powerful addition to the toolbox of orbital angular momentum and spin-orbit techniques that have already enabled many recent developments in quantum optics.

We experimentally study the violation of the CGLMP inequality for entangled 2-qubit and 2-qutrit states with different degrees of entanglement using numerically optimized measurement settings. The qudits are encoded and manipulated in the frequency spectrum of broadband energy-time entangled photons by taking into account a spatial light modulator. The latter allows to discretize the spectrum into bins. By controlling each frequency bin individually, the generation of maximally and non-maximally entangled qutrits is verified through quantum state tomography.