Show simple item record

dc.contributor.authorHolweck, F. G.
dc.contributor.authorSaniga, Metod
dc.contributor.authorLévay, Péter
dc.date.accessioned2013-12-09T12:00:01Z
dc.date.accessioned2016-10-05T14:13:57Z
dc.date.available2013-12-09T12:00:01Z
dc.date.available2016-10-05T14:13:57Z
dc.date.issued2013-12-09
dc.identifier.urihttp://publications.mfo.de/handle/mfo/1072
dc.descriptionResearch in Pairs 2013en_US
dc.description.abstractEmploying the fact that the geometry of the $N$-qubit ($N\geq 2$) Pauli group is embodied in the structure of the symplectic polar space $\mathcal{W}(2N-1, 2)$ and using properties of the Lagrangian Grassmannian $LGr(N, 2N)$ defined over the smallest Galois field, it is demonstrated that there exists a bijection between the set of maximum sets of mutually commuting elements of the $N$-qubit Pauli group and a certain subset of elements of the $2^{N-1}$-qubit Pauli group. In order to reveal finer traits of this correspondence, the cases $N=3$ (also addressed recently by Lévay, Planat and Saniga (JHEP 09 (2013) 037)) and $N=4$ are discussed in detail. As an apt application of our findings, we use the stratification of the ambient projective space $PG(2^N-1, 2)$ of the $2^{N-1}$-qubit Pauli group in terms of $G$-orbits, where $G\equiv SL(2,2) \times SL(2,2) \times \cdot \cdot \cdot \times SL(2,2) \rtimes S_N$, to decompose $\underline{\pi}(LGr(N,2N))$ into non-equivalent orbits. This leads to a partition of $LGr(N, 2N)$ into distinguished classes that can be labeled by elements of the above-mentioned Pauli groups.en_US
dc.language.isoenen_US
dc.publisherMathematisches Forschungsinstitut Oberwolfachen_US
dc.relation.ispartofseriesOberwolfach Preprints;2013,25
dc.subjectMulti-Qubiten_US
dc.subjectPauli Groupsen_US
dc.subjectSymplectic Polar Spaces W(2N − 1, 2)en_US
dc.subjectLagrangian Grassmannians LGr(N, 2N) over the smallest Galois fielden_US
dc.titleA Relation Between N-Qubit and 2N-1-Qubit Pauli Groups via Binary LGr(N,2N)en_US
dc.typePreprinten_US
dc.rights.licenseDieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.de
dc.rights.licenseThis document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.en
dc.identifier.doi10.14760/OWP-2013-25
local.scientificprogramResearch in Pairs 2013
local.series.idOWP-2013-25
dc.identifier.urnurn:nbn:de:101:1-2013120623145
dc.identifier.ppn1653153458


Files in this item

Thumbnail

This item appears in the following Collection(s)

Show simple item record