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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Exploiting Boron Coordination: B←N Bond Supports a [2+2] Photodimerization in the Solid State and Generation of a Diboron Bis‐Tweezer for Benzene/Thiophene Separation
Abstract B←N coordination supports a [2+2] photodimerization in the solid state. The bond is defined by an orthogonal interaction between stilbazole and a phenylboronic ester to enable a stereocontrolled and rapid photoreaction. The cyclobutane photoproduct affords a novel diboron bis‐tweezer adduct that is used to separate a mixture of benzene and thiophene upon crystallization.
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- Award ID(s):
- 1708673
- PAR ID:
- 10087912
- Publisher / Repository:
- Wiley Blackwell (John Wiley & Sons)
- Date Published:
- Journal Name:
- Angewandte Chemie International Edition
- Volume:
- 58
- Issue:
- 16
- ISSN:
- 1433-7851
- Page Range / eLocation ID:
- p. 5413-5416
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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