# Testing for entanglement with periodic coarse-graining. (arXiv:1506.01095v2 [quant-ph] UPDATED)

Continuous variables 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 novel
entanglement criteria based on a periodic structure of coarse-grained
measurements. The periodization of the measurements allows for 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 $\sim60\%$ relative to $7344$ studied
cases.