Peres–Horodecki criterion
E808788
entanglement criterion
mathematical criterion
result in quantum information theory
separability criterion
The Peres–Horodecki criterion is a fundamental test in quantum information theory that determines whether a given quantum state is entangled or separable by examining the positivity of its partial transpose.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Peres–Horodecki criterion canonical | 1 |
| Peres–Horodecki criterion for separability | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T9600464 — 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: Peres–Horodecki criterion Context triple: [Asher Peres, notableFor, Peres–Horodecki criterion]
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A.
Schmidt decomposition
The Schmidt decomposition is a mathematical technique in functional analysis and quantum information theory that expresses a bipartite vector (such as a quantum state) as a sum of orthogonal product states with nonnegative coefficients, revealing its entanglement structure.
-
B.
Clauser–Horne–Shimony–Holt inequality
The Clauser–Horne–Shimony–Holt inequality is a key formulation of Bell's inequality used in quantum mechanics to test the incompatibility of local hidden variable theories with the predictions of quantum entanglement.
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C.
Clauser–Horne inequality
The Clauser–Horne inequality is a fundamental Bell-type inequality in quantum mechanics used to experimentally test local realism against the predictions of quantum entanglement.
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D.
Kochen–Specker theorem
The Kochen–Specker theorem is a foundational result in quantum mechanics showing that it is impossible to assign consistent, noncontextual definite values to all quantum observables, thereby ruling out a broad class of hidden-variable theories.
-
E.
Flavors of Entanglement
Flavors of Entanglement is a studio album by Canadian singer-songwriter Alanis Morissette that blends alternative rock with electronic influences and introspective lyrics.
- 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: Peres–Horodecki criterion Target entity description: The Peres–Horodecki criterion is a fundamental test in quantum information theory that determines whether a given quantum state is entangled or separable by examining the positivity of its partial transpose.
-
A.
Schmidt decomposition
The Schmidt decomposition is a mathematical technique in functional analysis and quantum information theory that expresses a bipartite vector (such as a quantum state) as a sum of orthogonal product states with nonnegative coefficients, revealing its entanglement structure.
-
B.
Clauser–Horne–Shimony–Holt inequality
The Clauser–Horne–Shimony–Holt inequality is a key formulation of Bell's inequality used in quantum mechanics to test the incompatibility of local hidden variable theories with the predictions of quantum entanglement.
-
C.
Clauser–Horne inequality
The Clauser–Horne inequality is a fundamental Bell-type inequality in quantum mechanics used to experimentally test local realism against the predictions of quantum entanglement.
-
D.
Kochen–Specker theorem
The Kochen–Specker theorem is a foundational result in quantum mechanics showing that it is impossible to assign consistent, noncontextual definite values to all quantum observables, thereby ruling out a broad class of hidden-variable theories.
-
E.
Flavors of Entanglement
Flavors of Entanglement is a studio album by Canadian singer-songwriter Alanis Morissette that blends alternative rock with electronic influences and introspective lyrics.
- F. None of above. chosen
Statements (47)
| Predicate | Object |
|---|---|
| instanceOf |
entanglement criterion
ⓘ
mathematical criterion ⓘ result in quantum information theory ⓘ separability criterion ⓘ |
| alsoKnownAs |
PPT criterion
NERFINISHED
ⓘ
positive partial transpose criterion NERFINISHED ⓘ |
| appliesTo |
bipartite quantum states
ⓘ
density matrices ⓘ finite-dimensional Hilbert spaces ⓘ |
| basedOnConcept |
partial transpose of a density matrix
ⓘ
positivity of operators ⓘ |
| characterizes |
entangled states
ⓘ
separable states ⓘ |
| coreIdea |
check whether the partially transposed density matrix is positive semidefinite
ⓘ
take the partial transpose of the density matrix with respect to one subsystem ⓘ |
| criterionType |
necessary and sufficient for separability in 2×2 systems
ⓘ
necessary and sufficient for separability in 2×3 systems ⓘ necessary but not sufficient for separability in higher-dimensional systems ⓘ |
| extendedBy | Horodecki family NERFINISHED ⓘ |
| field |
quantum entanglement
ⓘ
quantum information theory ⓘ quantum mechanics ⓘ |
| formalism | density operator formalism ⓘ |
| hasConsequence |
defines the class of PPT states
ⓘ
reveals existence of bound entangled PPT states ⓘ |
| hasLimitation | fails to detect some entangled states in dimensions higher than 2×3 ⓘ |
| implies |
if partial transpose has a negative eigenvalue then the state is entangled
ⓘ
if partial transpose is positive in 2×2 or 2×3 then the state is separable ⓘ |
| influenced |
classification of quantum states by entanglement properties
ⓘ
development of entanglement theory ⓘ |
| introducedBy | Asher Peres NERFINISHED ⓘ |
| mathematicalOperation | matrix transposition on one subsystem ⓘ |
| namedAfter |
Asher Peres
NERFINISHED
ⓘ
Michał Horodecki NERFINISHED ⓘ Paweł Horodecki NERFINISHED ⓘ Ryszard Horodecki NERFINISHED ⓘ |
| originalPublication | Physical Review Letters NERFINISHED ⓘ |
| relatedTo |
bound entanglement
ⓘ
entanglement witnesses ⓘ positive partial transpose (PPT) states ⓘ quantum channel positivity ⓘ separability problem ⓘ |
| requires | spectral analysis of the partially transposed matrix ⓘ |
| usedFor |
analyzing bipartite mixed states
ⓘ
detecting entanglement ⓘ testing separability of quantum states ⓘ |
| yearProposed | 1996 ⓘ |
How these facts were elicited
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Input
Subject: Peres–Horodecki criterion Description of subject: The Peres–Horodecki criterion is a fundamental test in quantum information theory that determines whether a given quantum state is entangled or separable by examining the positivity of its partial transpose.
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Peres–Horodecki criterion for separability