Continuous-variable systems find valuable applications in quantum information processing. To deal with an infinite-dimensional Hilbert space, one in general has to handle large numbers of discretized measurements in tasks such as entanglement detection. Here we employ the continuous transverse spatial variables of photon pairs to experimentally demonstrate entanglement criteria based on a periodic structure of coarse-grained measurements. The periodization of the measurements allows an efficient evaluation of entanglement using spatial masks acting as mode analyzers over the entire transverse field distribution of the photons and without the need to reconstruct the probability densities of the conjugate continuous variables. Our experimental results demonstrate the utility of the derived criteria with a success rate in entanglement detection of $\sim 60\%$ relative to 7344 studied cases.

• Received 7 February 2018

DOI:https://doi.org/10.1103/PhysRevA.97.042312