Question: What is the difference between Quantum interference and classical "waves"?
About the article "Quantum mechanics", section "Quantum mechanics and classical physics".

Candidate passages:
 and classical physics.
Predictions of quantum mechanics have been verified experimentally to an extremely high degree of accuracy.
According to the correspondence principle between classical and quantum mechanics, all objects obey the laws of quantum mechanics, and classical mechanics is just an approximation for large systems of objects (or a statistical quantum mechanics of a large collection of particles).
The laws of classical mechanics thus follow from the laws of quantum mechanics as a statistical average at the limit of large systems or large quantum numbers.
However, chaotic systems do not have good quantum numbers, and quantum chaos studies the relationship between classical and quantum descriptions in these systems.
Quantum coherence is an essential difference between classical and quantum theories as illustrated by the Einstein–Podolsky–Rosen (EPR) paradox — an attempt to disprove quantum mechanics by an appeal to local realism.
Quantum interference involves adding together "probability amplitudes", whereas classical "waves" infer that there is an adding together of "intensities".
For microscopic bodies, the extension of the system is much smaller than the coherence length, which gives rise to long-range entanglement and other nonlocal phenomena characteristic of quantum systems.
Quantum coherence is not typically evident at macroscopic scales, though an exception to this rule may occur at extremely low temperatures (i.e.
approaching absolute zero) at which quantum behavior may manifest itself macroscopically.
This is in accordance with the following observations:
 Many macroscopic properties of a classical system are a direct consequence of the quantum behavior of its parts.
For example, the stability of bulk matter (consisting of atoms and molecules which would quickly collapse under electric forces alone), the rigidity of solids, and the mechanical, thermal, chemical, optical and magnetic properties of matter are all results of the interaction of electric charges under the rules of quantum mechanics.
 While the seemingly "exotic" behavior of matter posited by quantum mechanics and relativity theory become more apparent when dealing with particles of extremely small size or velocities approaching the speed of light, the laws of classical, often considered "Newtonian", physics remain accurate in predicting the behavior of the vast majority of "large" objects (on the order of the size of large molecules or bigger) at velocities much smaller than the velocity of light.
Since the Schrödinger equation is a wave equation and all objects can be considered waves in quantum mechanics, interference is ubiquitous.
Some examples: Bose–Einstein condensates can exhibit interference fringes.
Atomic populations show interference in a Ramsey interferometer.
Photons, atoms, electrons, neutrons, and molecules have exhibited interference in double-slit interferometers. 
The rules of quantum mechanics are highly successful in describing microscopic objects, atoms and elementary particles.
But "macroscopic systems", like springs and capacitors, are accurately described by classical theories like classical mechanics and classical electrodynamics.
If quantum mechanics were to be applicable to macroscopic objects, there must be some limit in which quantum mechanics reduces to classical mechanics.
"Bohr's correspondence principle demands that classical physics and quantum physics give the same answer when the systems become large".
The conditions under which quantum and classical physics agree are referred to as the correspondence limit, or the classical limit.
Bohr provided a rough prescription for the correspondence limit: it occurs "when the quantum numbers describing the system are large".
A more elaborated analysis of quantum-classical correspondence (QCC) in wavepacket spreading leads to the distinction between robust "restricted QCC" and fragile "detailed QCC".
"Restricted QCC" refers to the first two moments of the probability distribution and is true even when the wave packets diffract, while "detailed QCC" requires smooth potentials which vary over scales much larger than the wavelength, which is what Bohr considered.
The post-1925 new quantum theory came in two different formulations.
In matrix mechanics, the correspondence principle was built in and was used to construct the theory.
In the Schrödinger approach classical behavior is not clear because the waves spread out as they move.
Once the Schrödinger equation was given a probabilistic interpretation, Ehrenfest showed that Newton's laws hold on average: the quantum statistical expectation value of the position and momentum obey Newton's laws.
The correspondence principle is one of the tools available to physicists for selecting quantum theories corresponding to reality.
The principles of quantum mechanics are broad: states of a physical system form a complex vector space and physical observables are identified with Hermitian operators that act on this Hilbert space.
The correspondence principle limits the choices to those that reproduce classical mechanics in the correspondence limit.
Because quantum mechanics only reproduces classical mechanics in a statistical interpretation, and because the statistical interpretation only gives the probabilities of different classical outcomes, Bohr has argued that classical physics does not emerge from quantum physics in the same way that classical mechanics emerges as an approximation of special relativity at small velocities.
He argued that classical physics exists independently of quantum theory and cannot be derived from it.
His position is that it is inappropriate to understand the experiences of observers using purely quantum mechanical notions such as wavefunctions because the different states of experience of an observer are defined classically, and do not have a quantum mechanical analog.
The relative state interpretation of quantum mechanics is an attempt to understand the experience of observers using only quantum mechanical notions.
Niels Bohr was an early opponent of such interpretations.
Many of these conceptual problems, however, resolve in the phase-space formulation of quantum mechanics, where the "same variables with the same interpretation" are utilized to describe both quantum and classical mechanics. 
The interferometric visibility (also known as "interference visibility" or "fringe visibility" or just "visibility") quantifies the contrast of interference in any system which has wave-like properties, such as optics, quantum mechanics, water waves, or electrical signals.
Generally, two or more waves are combined and as the phase between them is changed (e.g.
in an interferometer) the power or intensity (probability or population in quantum mechanics) of the resulting wave oscillates (forming an interference pattern).
The ratio of the size or amplitude of these oscillations to the sum of the powers of the individual waves is defined as the visibility. 
The interference between two (or more) waves establishes a correlation between these waves.
In particle physics, in particular, where to each particle there is associated a wave, we encounter thus interference and correlations between two (or more) particles, described mathematically by second or higher order correlation functions.
These correlations have quite specific properties for identical particles.
We then distinguish Bose–Einstein correlations for bosons and Fermi–Dirac correlations for fermions.
While in Fermi–Dirac second order correlations the particles are antibunched, in Bose–Einstein correlations (BEC) they are bunched.
Another distinction between Bose–Einstein and Fermi–Dirac correlation is that only BEC can present quantum coherence (cf.
In optics two beams of light are said to interfere coherently, when the phase difference between their waves is constant; if this phase difference is random or changing the beams are incoherent.
The coherent superposition of wave amplitudes is called first order interference.
In analogy to that we have intensity or second order Hanbury Brown and Twiss (HBT) interference, which generalizes the interference between amplitudes to that between squares of amplitudes, i.e.
between intensities.
In optics amplitude interferometry is used for the determination of lengths, surface irregularities and indexes of refraction; intensity interferometry, besides presenting in certain cases technical advantages (like stability) as compared with amplitude interferometry, allows also the determination of quantum coherence of sources.