Asset Details
Do you wish to reserve the book?
Taxonomy of Polar Subspaces of Multi-Qubit Symplectic Polar Spaces of Small Rank
Hey, we have placed the reservation for you!
By the way, why not check out events that you can attend while you pick your title.
Oops! Something went wrong.
Looks like we were not able to place the reservation. Kindly try again later.
Are you sure you want to remove the book from the shelf?
Taxonomy of Polar Subspaces of Multi-Qubit Symplectic Polar Spaces of Small Rank
Do you wish to request the book?
Taxonomy of Polar Subspaces of Multi-Qubit Symplectic Polar Spaces of Small Rank
Please be aware that the book you have requested cannot be checked out. If you would like to checkout this book, you can reserve another copy
We have requested the book for you!
Your request is successful and it will be processed during the Library working hours. Please check the status of your request in My Requests.
Oops! Something went wrong.
Looks like we were not able to place your request. Kindly try again later.
Journal Article
Taxonomy of Polar Subspaces of Multi-Qubit Symplectic Polar Spaces of Small Rank
2021
Overview
We study certain physically-relevant subgeometries of binary symplectic polar spaces W(2N−1,2) of small rank N, when the points of these spaces canonically encode N-qubit observables. Key characteristics of a subspace of such a space W(2N−1,2) are: the number of its negative lines, the distribution of types of observables, the character of the geometric hyperplane the subspace shares with the distinguished (non-singular) quadric of W(2N−1,2) and the structure of its Veldkamp space. In particular, we classify and count polar subspaces of W(2N−1,2) whose rank is N−1. W(3,2) features three negative lines of the same type and its W(1,2)’s are of five different types. W(5,2) is endowed with 90 negative lines of two types and its W(3,2)’s split into 13 types. A total of 279 out of 480 W(3,2)’s with three negative lines are composite, i.e., they all originate from the two-qubit W(3,2). Given a three-qubit W(3,2) and any of its geometric hyperplanes, there are three other W(3,2)’s possessing the same hyperplane. The same holds if a geometric hyperplane is replaced by a ‘planar’ tricentric triad. A hyperbolic quadric of W(5,2) is found to host particular sets of seven W(3,2)’s, each of them being uniquely tied to a Conwell heptad with respect to the quadric. There is also a particular type of W(3,2)’s, a representative of which features a point each line through which is negative. Finally, W(7,2) is found to possess 1908 negative lines of five types and its W(5,2)’s fall into as many as 29 types. A total of 1524 out of 1560 W(5,2)’s with 90 negative lines originate from the three-qubit W(5,2). Remarkably, the difference in the number of negative lines for any two distinct types of four-qubit W(5,2)’s is a multiple of four.
Publisher
MDPI AG,MDPI
