Families of Perfect Tensors
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 (ℂ^d)^⊗ 4 using exponential maps from Lie theory. With this method, we find explicit examples of non-classical perfect tensors in (ℂ^3)^⊗ 4. In particular, we answer an open question posted by Życzkowski et al.
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