The difference between classical and quantum correlations

I believe it is an important topic for us to learn about. There are frequent mistakes, people confuse many times classical correlations with quantum entanglement on their blogs and forums and only peer-reviewed papers give the true answers.

Classical correlations exist between the quanta of a single mode generated with resonance, like in the case of lasers and musical instruments.

They are called Coherent Gaussian Beams, appear when the individual waves of a pulse are in phase (0 degrees phase difference) and are described by different equations from the ones that describe quantum entanglement.

If classical correlations and quantum entanglement were the same, you would just have to use a single laser device to generate billions of entangled photons, without use of beam splitter or nonlinear crystals. But they aren't.

While I know about the difference between quantum and classical correlations, I do not know how to distinguish them in practice.

Can you please give some examples of interactions that create these types of correlations for each case, so that everyone may have in future a template to follow in their experiments?

1. Classical correlations: resonant excitations...
2. Quantum correlations: parametric fluorescence, double decay...
 
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