  Entangled coherent states, which can in principle be created using strong
Kerr non-linearities, allow the violation of Bell inequalities for very
coarse-grained measurements. This seems to contradict a recent conjecture that
observing quantum effects in macroscopic systems generally requires very
precise measurements. However, here we show that both the creation of the
required states and the required measurements rely on being able to control the
phase of the necessary Kerr-nonlinearity based unitary operations with extreme
precision. This lends support to the idea that there is a general principle
that makes macroscopic quantum effects difficult to observe, even in the
absence of decoherence.
