Question: How different are Quantum interference and classical waves?
About the article "Quantum mechanics", section "Quantum mechanics and classical physics".

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Quantum walks exhibit very different features from classical random walks.
In particular, they do not converge to limiting distributions and due to the power of quantum interference they may spread significantly faster or slower than their classical equivalents. 
To examine how decoherence operates, an "intuitive" model is presented.
The model requires some familiarity with quantum theory basics.
Analogies are made between visualisable classical phase spaces and Hilbert spaces.
A more rigorous derivation in Dirac notation shows how decoherence destroys interference effects and the "quantum nature" of systems.
Next, the density matrix approach is presented for perspective. 
Diffraction refers to various phenomena which occur when a wave encounters an obstacle or a slit.
In classical physics, the diffraction phenomenon is described as the apparent bending of waves around small obstacles and the spreading out of waves past small openings.
These characteristic behaviors are exhibited when a wave encounters an obstacle or a slit that is comparable in size to its wavelength.
Similar effects occur when a light wave travels through a medium with a varying refractive index, or when a sound wave travels through a medium with varying acoustic impedance.
Diffraction occurs with all waves, including sound waves, water waves, and electromagnetic waves such as visible light, X-rays and radio waves.
Since physical objects have wave-like properties (at the atomic level), diffraction also occurs with matter and can be studied according to the principles of quantum mechanics.
Italian scientist Francesco Maria Grimaldi coined the word "diffraction" and was the first to record accurate observations of the phenomenon in 1660.
Richard Feynman wrote: He suggested that when there are only a few sources, say two, we call it interference, as in Young's slits, but with a large number of sources, the process is labelled diffraction.
While diffraction occurs whenever propagating waves encounter such changes, its effects are generally most pronounced for waves whose wavelength is roughly comparable to the dimensions of the diffracting object or slit.
If the obstructing object provides multiple, closely spaced openings, a complex pattern of varying intensity can result.
This is due to the superposition, or interference, of different parts of a wave that travels to the observer by different paths (see diffraction grating).
The formalism of diffraction can also describe the way in which waves of finite extent propagate in free space.
For example, the expanding profile of a laser beam, the beam shape of a radar antenna and the field of view of an ultrasonic transducer can all be analyzed using diffraction equations. 
In physics, coherence is an ideal property of waves that enables stationary (i.e.
temporally and spatially constant) interference.
It contains several distinct concepts, which are limit cases that never occur in reality but allow an understanding of the physics of waves, and has become a very important concept in quantum physics.
More generally, coherence describes all properties of the correlation between physical quantities of a single wave, or between several waves or wave packets.
Interference is nothing more than the addition, in the mathematical sense, of wave functions.
In quantum mechanics, a single wave can interfere with itself, but this is due to its quantum behavior and is still an addition of two waves (see Young's slits experiment).
This implies that constructive or destructive interferences are limit cases, and that waves can always interfere, even if the result of the addition is complicated or not remarkable.
When interfering, two waves can add together to create a wave of greater amplitude than either one (constructive interference) or subtract from each other to create a wave of lesser amplitude than either one (destructive interference), depending on their relative phase.
Two waves are said to be coherent if they have a constant relative phase.
The degree of coherence is measured by the interference visibility, a measure of how perfectly the waves can cancel due to destructive interference.
Spatial coherence describes the correlation between waves at different points in space.
Temporal coherence describes the correlation or predictable relationship between waves observed at different moments in time.
Both are observed in the Michelson–Morley experiment and Young's interference experiment.
Once the fringes are obtained in the Michelson–Morley experiment, when one of the mirrors is moved away gradually, the time for the beam to travel increases and the fringes become dull and finally are lost, showing temporal coherence.
Similarly, if in Young's double slit experiment the space between the two slits is increased, the coherence dies gradually and finally the fringes disappear, showing spatial coherence. 
Elementary precursors to current quantum eraser experiments such as the "simple quantum eraser" described above have straightforward classical-wave explanations.
Indeed, it could be argued that there is nothing particularly quantum about this experiment.
Nevertheless, Jordan has argued on the basis of the correspondence principle, that despite the existence of classical explanations, first-order interference experiments such as the above can be interpreted as true quantum erasers.
These precursors use single-photon interference.
Versions of the quantum eraser using entangled photons, however, are intrinsically non-classical.
Because of that, in order to avoid any possible ambiguity concerning the quantum versus classical interpretation, most experimenters have opted to use nonclassical entangled-photon light sources to demonstrate quantum erasers with no classical analog.
Furthermore, use of entangled photons enables the design and implementation of versions of the quantum eraser that are impossible to achieve with single-photon interference, such as the delayed choice quantum eraser which is the topic of this article.