von Neumann entropy
E590895
Von Neumann entropy is a measure of quantum uncertainty or mixedness of a quantum state, generalizing classical Shannon entropy to density matrices in quantum mechanics and quantum information theory.
All labels observed (1)
| Label | Occurrences |
|---|---|
| von Neumann entropy canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T6397156 — 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: von Neumann entropy Context triple: [Page curve, usesConcept, von Neumann entropy]
-
A.
Rényi entropy
Rényi entropy is a generalized measure of information and uncertainty that extends Shannon entropy by introducing a tunable order parameter to emphasize different aspects of a probability distribution.
-
B.
Shannon entropy
Shannon entropy is a fundamental measure in information theory that quantifies the average uncertainty or information content in a random variable or message source.
-
C.
Rényi divergence
Rényi divergence is a family of information-theoretic measures that generalize Kullback–Leibler divergence to quantify the dissimilarity between probability distributions, parameterized by an order α.
-
D.
Tsallis entropy
Tsallis entropy is a generalized, nonadditive entropy measure in statistical mechanics and information theory that extends Shannon entropy to better describe complex, nonextensive systems.
-
E.
Shannon–Khinchin axioms
The Shannon–Khinchin axioms are a set of fundamental conditions that uniquely characterize Shannon entropy as the standard measure of information and uncertainty in probability theory and information theory.
- 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: von Neumann entropy Target entity description: Von Neumann entropy is a measure of quantum uncertainty or mixedness of a quantum state, generalizing classical Shannon entropy to density matrices in quantum mechanics and quantum information theory.
-
A.
Rényi entropy
Rényi entropy is a generalized measure of information and uncertainty that extends Shannon entropy by introducing a tunable order parameter to emphasize different aspects of a probability distribution.
-
B.
Shannon entropy
Shannon entropy is a fundamental measure in information theory that quantifies the average uncertainty or information content in a random variable or message source.
-
C.
Rényi divergence
Rényi divergence is a family of information-theoretic measures that generalize Kullback–Leibler divergence to quantify the dissimilarity between probability distributions, parameterized by an order α.
-
D.
Tsallis entropy
Tsallis entropy is a generalized, nonadditive entropy measure in statistical mechanics and information theory that extends Shannon entropy to better describe complex, nonextensive systems.
-
E.
Shannon–Khinchin axioms
The Shannon–Khinchin axioms are a set of fundamental conditions that uniquely characterize Shannon entropy as the standard measure of information and uncertainty in probability theory and information theory.
- F. None of above. chosen
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
information-theoretic quantity
ⓘ
quantum entropy measure ⓘ |
| additivityCondition | additive for product states: S(ρ⊗σ) = S(ρ)+S(σ) ⓘ |
| alternativeLogarithmBase | e ⓘ |
| alternativeUnit | nat ⓘ |
| appliesTo |
density matrix
ⓘ
density operator ⓘ |
| characterizes |
mixedness of a quantum state
ⓘ
quantum uncertainty ⓘ |
| classicalLimit | reduces to Shannon entropy for commuting density matrices ⓘ |
| context |
black hole entropy and holography
ⓘ
quantum thermodynamics ⓘ |
| definedOn | trace-class operators on Hilbert space ⓘ |
| definition | S(ρ) = -Tr(ρ log ρ) ⓘ |
| domain | quantum states ⓘ |
| equals | Shannon entropy of eigenvalue distribution of ρ ⓘ |
| field |
quantum information theory
ⓘ
quantum mechanics ⓘ statistical mechanics ⓘ |
| generalizes | Shannon entropy NERFINISHED ⓘ |
| isPositiveFor | mixed states ⓘ |
| isZeroFor | pure states ⓘ |
| maximumCondition | maximal for maximally mixed state on a given Hilbert space ⓘ |
| maximumValue | log d for maximally mixed state on d-dimensional Hilbert space ⓘ |
| monotoneUnder | completely positive trace-preserving maps for appropriate combinations ⓘ |
| namedAfter | John von Neumann NERFINISHED ⓘ |
| nonNegativity | S(ρ) ≥ 0 ⓘ |
| property |
concave in the density operator
ⓘ
unitarily invariant ⓘ |
| relatedConcept |
Rényi entropy
NERFINISHED
ⓘ
entanglement entropy ⓘ relative entropy ⓘ |
| requires |
spectral decomposition of density operator
ⓘ
trace operation ⓘ |
| satisfies |
Araki–Lieb inequality
NERFINISHED
ⓘ
strong subadditivity ⓘ subadditivity ⓘ |
| symbol |
S
ⓘ
S(ρ) ⓘ |
| typicalUnit | bit ⓘ |
| usedFor |
Holevo bound
NERFINISHED
ⓘ
defining coherent information ⓘ defining quantum conditional entropy ⓘ defining quantum mutual information ⓘ entanglement measures ⓘ quantum channel capacity formulas ⓘ quantum data compression ⓘ |
| usesLogarithmBase | 2 ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: von Neumann entropy Description of subject: Von Neumann entropy is a measure of quantum uncertainty or mixedness of a quantum state, generalizing classical Shannon entropy to density matrices in quantum mechanics and quantum information theory.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.