nonclassicality

Nonclassicality is a term used in quantum physics to describe properties of physical states that cannot be explained by classical physics. In quantum optics, it designates light fields whose statistical or phase-space properties lack a classical counterpart and cannot be described by a positive, well-behaved probability distribution over coherent states.

A common formalism is the Glauber-Sudarshan P representation. Any quantum state ρ of a single mode can be written as ρ = ∫ P(α) |α><α| d^2α, where |α> are coherent states. If P(α) is a genuine probability distribution, the state is classical; if P is highly singular or takes negative values, the state is nonclassical. Other practical indicators include Wigner function negativity and non-Gaussian features.

Signatures of nonclassicality include sub-Poissonian photon statistics (Mandel Q parameter < 0), quadrature squeezing (noise in one field quadrature below the vacuum level), and negative regions in the Wigner function. A variety of criteria and inequalities, such as those due to Hillery-Zubairy or Vogel, provide operational tests for nonclassical behavior. It is important to note that Wigner negativity is a strong but not necessary condition for nonclassicality; some nonclassical states have positive Wigner functions, while P-function negativity remains a robust marker.

Examples range from single-photon Fock states and Schrödinger cat states (often exhibit Wigner negativity) to squeezed states (nonclassical in origin, though their Wigner function can be positive). Nonclassicality is a resource in quantum information, metrology, and communication and is distinct from, yet related to, entanglement, as it can occur in single modes as well as in multipartite systems.