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Families of Perfect Tensors (2211.15776v3)
Published 28 Nov 2022 in math.AG, cs.IT, math.IT, and quant-ph
Abstract: Perfect tensors are the tensors corresponding to the absolutely maximally entangled states, a special type of quantum states of interest in quantum information theory. We establish a method to compute parameterized families of perfect tensors in $(\mathbb{C}d){\otimes 4}$ using exponential maps from Lie theory. With this method, we find explicit examples of non-classical perfect tensors in $(\mathbb{C}3){\otimes 4}$. In particular, we answer an open question posted by .Zyczkowski et al.
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