Families of Perfect Tensors

TL;DR

This paper introduces a Lie-theoretic method to construct families of perfect tensors, providing explicit examples in four-partite systems and answering an open question in quantum information theory.

Contribution

It develops a novel approach using exponential maps from Lie theory to generate perfect tensors in complex four-partite systems, including non-classical examples.

Findings

Explicit construction of perfect tensors in $(\\mathbb{C}^3)^{\\otimes 4}$

Introduction of a Lie-theoretic method for tensor generation

Resolution of an open question by \.Zyczkowski et al.

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.