We derive reliable entanglement witnesses for coarse--grained measurements on
continuous variable systems. These witnesses never return a "false positive"
for identification of entanglement, under any degree of coarse graining. We
show that, even in the case of Gaussian states, entanglement witnesses based on
the Shannon entropy can outperform those based on variances. We apply our
results to experimental identification of spatial entanglement of photon pairs.Comment: Dedicated to Iwo Bialynicki-Birula on his 80th birthday, who inspired
much of this wor
