Universal points in the asymptotic spectrum of tensors

The asymptotic restriction problem for tensors is to decide, given $s$ and $t$, whether the nth tensor power of can be obtained from $(n+o(n))$th t by applying linear maps legs (this we call restriction), when $n$ goes infinity. In this context, Volker Strassen, striving understand complexity matrix multiplication, introduced in 1986 spectrum tensors. Essentially, a family $X$, closed under direct sum product, reduces finding all $X$ reals that are monotone restriction, normalised on diagonal tensors, additive multiplicative which Strassen named spectral points. created support functionals, points oblique strict subfamily Universal construction nontrivial universal has been an open more than thirty years. We construct first time over complex numbers, using quantum entropy covariants: functionals. process connect marginal entanglement polytope. To demonstrate spectrum, reprove (in hindsight) recent results cap set reducing computing reduced polynomial multiplication tensor, prime example Strassen. A better understanding our may lead further progress related questions. additionally show functionals characterise slice rank