English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

The geometry of the real four-qubit Pauli group, being embodied in thestructure of the symplectic polar space W(7,2), is analyzed in terms of ovoidsof a hyperbolic quadric of PG(7,2), the seven-dimensional projective space oforder two. The quadric is selected in such a way that it contains all 135symmetric elements of the group. Under such circumstances, the third element onthe line defined by any two points of an ovoid is skew-symmetric, as is thenucleus of the conic defined by any three points of an ovoid. Each ovoid thusyields 36/84 elements of the former/latter type, accounting for all 120skew-symmetric elements of the group. There are a number of notable types ofovoid-associated subgeometries of the group, of which we mention the following:a subset of 12 skew-symmetric elements lying on four mutually skew lines thatspan the whole ambient space, a subset of 15 symmetric elements thatcorresponds to two ovoids sharing three points, a subset of 19 symmetricelements generated by two ovoids on a common point, a subset of 27 symmetricelements that can be partitioned into three ovoids in two unique ways, a subsetof 27 skew-symmetric elements that exhibits a 15 + 2 x 6 split reminding thatexhibited by an elliptic quadric of PG(5,2), and a subset of sevenskew-symmetric elements formed by the nuclei of seven conics having two pointsin common, which is an analogue of a Conwell heptad of PG(5,2).  The strategy we employed is completely novel and unique in its nature, as arethe results obtained. Such a detailed dissection of the geometry of the groupin question may, for example, be crucial in getting further insights into thestill-puzzling black-hole-qubit correspondence/analogy.

Charting the Real Four-Qubit Pauli Group via Ovoids of a Hyperbolic Quadric of PG(7,2)