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.
Observed surface forms (1)
| Surface form | Occurrences |
|---|---|
| Peres–Horodecki criterion for separability | 1 |
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 ⓘ |
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