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2017

Dimension towers of SICs. I. Aligned SICs and embedded tight frames

Appleby, Marcus, Bengtsson, Ingemar, Dumitru, Irina et al.

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Algebraic number theory relates SIC-POVMs in dimension $d>3$ to those in dimension $d(d-2)$.

We define a SIC in dimension $d(d-2)$ to be aligned to a SIC in dimension $d$ if and only if the squares of the overlap phases in dimension $d$ appear as a subset of the overlap phases in dimension $d(d-2)$ in a specified way.
We give 19 (mostly numerical) examples of aligned SICs.
We conjecture that given any SIC in dimension $d$ there exists an aligned SIC in dimension $d(d-2)$.

Dimension towers of SICs. I. Aligned SICs and embedded tight frames · Around

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