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Title: A note on tight projective 2‐designs
Abstract

We study tight projective 2‐designs in three different settings. In the complex setting, Zauner's conjecture predicts the existence of a tight projective 2‐design in every dimension. Pandey, Paulsen, Prakash, and Rahaman recently proposed an approach to make quantitative progress on this conjecture in terms of the entanglement breaking rank of a certain quantum channel. We show that this quantity is equal to the size of the smallest weighted projective 2‐design. Next, in the finite field setting, we introduce a notion of projective 2‐designs, we characterize when such projective 2‐designs are tight, and we provide a construction of such objects. Finally, in the quaternionic setting, we show that every tight projective 2‐design for determines an equi‐isoclinic tight fusion frame of subspaces of of dimension 3.

 
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Award ID(s):
1829955
NSF-PAR ID:
10449865
Author(s) / Creator(s):
 ;  ;  
Publisher / Repository:
Wiley Blackwell (John Wiley & Sons)
Date Published:
Journal Name:
Journal of Combinatorial Designs
Volume:
29
Issue:
12
ISSN:
1063-8539
Page Range / eLocation ID:
p. 809-832
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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