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Ghost imaging is the remarkable process where an image can be formed from photons that have not "seen" the object. Traditionally this phenomenon has required initially correlated but spatially separated photons, e.g., one to interact with the object and the other to form the image, and has been observed in many physical situations, spanning both the quantum and classical regimes. To date, all instances of ghost imaging record an image with the same contrast as the object, i.e., where the object is bright, the image is also bright, and vice versa. Here we observe ghost imaging in a new system - a system based on photons that have never interacted. We utilise entanglement swapping between independent pairs of spatially entangled photons to establish position correlations between two initially independent photons. As a consequence of an anti-symmetric projection in the entanglement swapping process, the recorded image is the contrast reversed version of the object, i.e., where the object is bright, the image is dark, and vice versa. The results highlight the importance of state projection in this ghost imaging process and provides a pathway to teleporting images across a quantum network.

The problem of using observed correlations to infer causal relations is relevant to a wide variety of scientific disciplines. Yet given correlations between just two classical variables, it is impossible to determine whether they arose from a causal influence of one on the other or a common cause influencing both, unless one can implement a randomized intervention. We here consider the problem of causal inference for quantum variables. We introduce causal tomography, which unifies and generalizes conventional quantum tomography schemes to provide a complete solution to the causal inference problem using a quantum analogue of a randomized trial. We furthermore show that, in contrast to the classical case, observed quantum correlations alone can sometimes provide a solution. We implement a quantum-optical experiment that allows us to control the causal relation between two optical modes, and two measurement schemes -- one with and one without randomization -- that extract this relation from the observed correlations. Our results show that entanglement and coherence, known to be central to quantum information processing, also provide a quantum advantage for causal inference., Comment: 17 pages, 6 figures. Comments welcome

Orbital angular momentum (OAM) entanglement is investigated in the Bessel-Gauss (BG) basis. Having a readily adjustable radial scale, BG modes provide a more favourable basis for OAM entanglement over Laguerre-Gaussian (LG) modes. The OAM bandwidth in terms of BG modes can be increased by selection of particular radial modes and leads to a flattening of the spectrum. The flattening of the spectrum allows for higher entanglement. We demonstrate increased entanglement in terms of BG modes by performing a Bell-type experiment and violating the appropriate Clauser Horne Shimony Holt (CHSH) inequality. In addition, we reconstruct the quantum state of BG modes entangled in high-dimensions., Comment: 8 pages, 4 figures

The controlled generation of entangled states and their subsequent detection are integral aspects of quantum information science. In this work, we analyse the application of nonlinear witnesses to the verification of entanglement, and we demonstrate experimentally that nonlinear witnesses perform significantly better than linear witnesses. Specifically, we demonstrate that a single non- linear entanglement witness is able to determine to a high degree of certainty that a mixed state containing orbital angular momentum (OAM) entanglement of specific forms is entangled for any relative phase and sufficient fidelity. This is a significant improvement over linear witnesses, which cannot provide the same level of performance. We envisage that nonlinear witnesses and our method of state preparation will have further uses in areas of quantum science such as superdense coding and quantum key distribution.