dc.contributor.author Holweck, F. G. dc.contributor.author Saniga, Metod dc.contributor.author Lévay, Péter dc.date.accessioned 2013-12-09T12:00:01Z dc.date.accessioned 2016-10-05T14:13:57Z dc.date.available 2013-12-09T12:00:01Z dc.date.available 2016-10-05T14:13:57Z dc.date.issued 2013-12-09 dc.identifier.uri http://publications.mfo.de/handle/mfo/1072 dc.description Research in Pairs 2013 en_US dc.description.abstract Employing 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.iso en en_US dc.publisher Mathematisches Forschungsinstitut Oberwolfach en_US dc.relation.ispartofseries Oberwolfach Preprints;2013,25 dc.subject Multi-Qubit en_US dc.subject Pauli Groups en_US dc.subject Symplectic Polar Spaces W(2N − 1, 2) en_US dc.subject Lagrangian Grassmannians LGr(N, 2N) over the smallest Galois field en_US dc.title A Relation Between N-Qubit and 2N-1-Qubit Pauli Groups via Binary LGr(N,2N) en_US dc.type Preprint en_US dc.rights.license Dieses 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.license This 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.doi 10.14760/OWP-2013-25 local.scientificprogram Research in Pairs 2013 local.series.id OWP-2013-25 dc.identifier.urn urn:nbn:de:101:1-2013120623145 dc.identifier.ppn 1653153458
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