Wigner distribution function

E98266

mathematical concept phase-space distribution quasi-probability distribution tool in quantum mechanics tool in signal processing

The Wigner distribution function is a quasi-probability distribution used in quantum mechanics and signal processing to represent quantum states in phase space, often exhibiting non-classical features such as negative values.

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All labels observed (7)

Label	Occurrences
Wigner distribution function canonical	2
Wigner function	2
Wigner functions	1
Wigner quasi-probability distribution	1
Wigner–Ville distribution	1
Wigner–Weyl transform	1
discrete Wigner function	1

How this entity was disambiguated

This entity first appeared as the object of triple T818208 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.

NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07

Target entity: Wigner distribution function
Context triple: [Eugene Wigner, knownFor, Wigner distribution function]

A. Fokker–Planck equation
The Fokker–Planck equation is a partial differential equation that describes the time evolution of the probability density function of a stochastic (random) process, such as Brownian motion.
B. Wick’s theorem
Wick’s theorem is a fundamental result in quantum field theory that expresses time-ordered products of field operators as sums of normal-ordered products with all possible contractions, forming the basis for deriving Feynman rules and diagrammatic expansions.
C. Fourier analysis
Fourier analysis is a mathematical method for decomposing functions or signals into sums of sinusoidal components, widely used in fields such as signal processing, physics, and engineering.
D. Fourier
Fourier is a French surname most famously associated with Jean-Baptiste Joseph Fourier, the mathematician and physicist known for developing Fourier analysis and Fourier series.
E. Fresnel diffraction theory
Fresnel diffraction theory is a wave-optics framework that describes how light diffracts when source or observation distances are finite, using near-field approximations derived from the Huygens–Fresnel principle.
F. None of above. chosen
G. Unsure - the case is ambiguous/there is not enough information to decide.

NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07

Target entity: Wigner distribution function
Target entity description: The Wigner distribution function is a quasi-probability distribution used in quantum mechanics and signal processing to represent quantum states in phase space, often exhibiting non-classical features such as negative values.

A. Fokker–Planck equation
The Fokker–Planck equation is a partial differential equation that describes the time evolution of the probability density function of a stochastic (random) process, such as Brownian motion.
B. Wick’s theorem
Wick’s theorem is a fundamental result in quantum field theory that expresses time-ordered products of field operators as sums of normal-ordered products with all possible contractions, forming the basis for deriving Feynman rules and diagrammatic expansions.
C. Fourier analysis
Fourier analysis is a mathematical method for decomposing functions or signals into sums of sinusoidal components, widely used in fields such as signal processing, physics, and engineering.
D. Fourier
Fourier is a French surname most famously associated with Jean-Baptiste Joseph Fourier, the mathematician and physicist known for developing Fourier analysis and Fourier series.
E. Fresnel diffraction theory
Fresnel diffraction theory is a wave-optics framework that describes how light diffracts when source or observation distances are finite, using near-field approximations derived from the Huygens–Fresnel principle.
F. None of above. chosen

Statements (47)

Predicate	Object
instanceOf	mathematical concept ⓘ phase-space distribution ⓘ quasi-probability distribution ⓘ tool in quantum mechanics ⓘ tool in signal processing ⓘ
definedOn	phase space ⓘ
domain	position and momentum variables ⓘ
field	quantum mechanics ⓘ signal processing ⓘ time–frequency analysis ⓘ
generalizationOf	classical phase-space distribution ⓘ
hasApplication	quantum information processing ⓘ quantum state reconstruction ⓘ radar signal processing ⓘ speech analysis ⓘ time–frequency filtering ⓘ
hasProperty	bilinear in the wavefunction ⓘ can exhibit interference fringes ⓘ can take negative values ⓘ covariant under phase-space translations ⓘ marginals reproduce position and momentum distributions ⓘ non-classical features ⓘ normalized to one for pure states ⓘ not a true probability distribution ⓘ real-valued function ⓘ satisfies quantum Liouville equation ⓘ
introducedBy	Eugene Wigner ⓘ
introducedIn	1932 ⓘ
namedAfter	Eugene Wigner ⓘ
relatedTo	Glauber–Sudarshan P function ⓘ Husimi Q function ⓘ Moyal bracket ⓘ Weyl transform ⓘ linked to: Weyl quantization Weyl–Wigner phase-space formulation of quantum mechanics ⓘ linked to: Weyl quantization Wigner–Ville distribution ⓘ linked to: Wigner distribution function
represents	quantum states in phase space ⓘ time–frequency content of signals ⓘ
satisfies	correct classical limit for large quantum numbers ⓘ
usedFor	analyzing non-classical states of light ⓘ quantum chaos studies ⓘ quantum optics ⓘ quantum tomography ⓘ semiclassical approximations ⓘ signal analysis with high time–frequency resolution ⓘ studying quantum coherence ⓘ time–frequency representation of signals ⓘ visualizing quantum states ⓘ

How these facts were elicited