Matches in SemOpenAlex for { <https://semopenalex.org/work/W4293729939> ?p ?o ?g. }
Showing items 1 to 49 of
49
with 100 items per page.
- W4293729939 abstract "In $3times 3$ dimensions, entangled mixed states that are positive under partial transposition (PPT states) must have rank at least four. They are well understood. We say that they have rank $(4,4)$ since a state $rho$ and its partial transpose $rho^P$ both have rank four. The next problem is to understand the extremal PPT states of rank $(5,5)$. We call two states $textrm{SL}otimestextrm{SL}$-equivalent if they are related by a product transformation. A generic rank $(5,5)$ PPT state $rho$ is extremal, and $rho$ and $rho^P$ both have six product vectors in their ranges, and no product vectors in their kernels. The three numbers ${6,6;0}$ are $textrm{SL}otimestextrm{SL}$-invariants that help us classify the state. We have studied numerically a few types of nongeneric rank five PPT states, in particular states with one or more product vectors in their kernels. We find an interesting new analytical construction of all rank four extremal PPT states, up to $textrm{SL}otimestextrm{SL}$-equivalence, where they appear as boundary states on one single five dimensional face on the set of normalized PPT states. We say that a state $rho$ is $textrm{SL}otimestextrm{SL}$-symmetric if $rho$ and $rho^P$ are $textrm{SL}otimestextrm{SL}$-equivalent, and is genuinely $textrm{SL}otimestextrm{SL}$-symmetric if it is $textrm{SL}otimestextrm{SL}$-equivalent to a state $tau$ with $tau=tau^P$. Genuine $textrm{SL}otimestextrm{SL}$-symmetry implies a special form of $textrm{SL}otimestextrm{SL}$-symmetry. We have produced numerically a random sample of rank $(5,5)$ $textrm{SL}otimestextrm{SL}$-symmetric states. About fifty of these are of type ${6,6;0}$, among those all are extremal and about half are genuinely $textrm{SL}otimestextrm{SL}$-symmetric." @default.
- W4293729939 created "2022-08-31" @default.
- W4293729939 creator A5011429346 @default.
- W4293729939 creator A5087292943 @default.
- W4293729939 date "2017-06-23" @default.
- W4293729939 modified "2023-09-30" @default.
- W4293729939 title "Nongeneric positive partial transpose states of rank five in $3times 3$ dimensions" @default.
- W4293729939 doi "https://doi.org/10.48550/arxiv.1706.07671" @default.
- W4293729939 hasPublicationYear "2017" @default.
- W4293729939 type Work @default.
- W4293729939 citedByCount "0" @default.
- W4293729939 crossrefType "posted-content" @default.
- W4293729939 hasAuthorship W4293729939A5011429346 @default.
- W4293729939 hasAuthorship W4293729939A5087292943 @default.
- W4293729939 hasBestOaLocation W42937299391 @default.
- W4293729939 hasConcept C11413529 @default.
- W4293729939 hasConcept C114614502 @default.
- W4293729939 hasConcept C121332964 @default.
- W4293729939 hasConcept C164226766 @default.
- W4293729939 hasConcept C2524010 @default.
- W4293729939 hasConcept C33923547 @default.
- W4293729939 hasConcept C37914503 @default.
- W4293729939 hasConcept C48103436 @default.
- W4293729939 hasConcept C90673727 @default.
- W4293729939 hasConceptScore W4293729939C11413529 @default.
- W4293729939 hasConceptScore W4293729939C114614502 @default.
- W4293729939 hasConceptScore W4293729939C121332964 @default.
- W4293729939 hasConceptScore W4293729939C164226766 @default.
- W4293729939 hasConceptScore W4293729939C2524010 @default.
- W4293729939 hasConceptScore W4293729939C33923547 @default.
- W4293729939 hasConceptScore W4293729939C37914503 @default.
- W4293729939 hasConceptScore W4293729939C48103436 @default.
- W4293729939 hasConceptScore W4293729939C90673727 @default.
- W4293729939 hasLocation W42937299391 @default.
- W4293729939 hasOpenAccess W4293729939 @default.
- W4293729939 hasPrimaryLocation W42937299391 @default.
- W4293729939 hasRelatedWork W1978042415 @default.
- W4293729939 hasRelatedWork W2017331178 @default.
- W4293729939 hasRelatedWork W2087081347 @default.
- W4293729939 hasRelatedWork W2088849544 @default.
- W4293729939 hasRelatedWork W2327188743 @default.
- W4293729939 hasRelatedWork W2963179930 @default.
- W4293729939 hasRelatedWork W2976797620 @default.
- W4293729939 hasRelatedWork W3086542228 @default.
- W4293729939 hasRelatedWork W3102272702 @default.
- W4293729939 hasRelatedWork W4234996786 @default.
- W4293729939 isParatext "false" @default.
- W4293729939 isRetracted "false" @default.
- W4293729939 workType "article" @default.