Nonclassical light is light that cannot be described using classical electromagnetism; its characteristics are described by the quantized electromagnetic field and quantum mechanics.
The most common described forms of nonclassical light are the following:
The density matrix for any state of light can be written as:
where is a coherent state. A classical state of light is one in which is a probability density function. If it is not, the state is said to be nonclassical.[2]
Aspects of that would make it nonclassical are:
The matter is not quite simple. According to Mandel and Wolf: "The different coherent states are not [mutually] orthogonal, so that even if behaved like a true probability density [function], it would not describe probabilities of mutually exclusive states."[2]
Mandel, L.; Wolf, E. (1995), Optical Coherence and Quantum Optics, Cambridge UK: Cambridge University Press, ISBN 0-521-41711-2