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Quantum Control Electronics System Integration

Transversal gates of the ((3,3,2)) qutrit code and local symmetries of the absolutely maximally entangled state of four qutrits

arXiv
Authors: Ian Tan

Year

2026

Paper ID

3263

Status

Preprint

Abstract Read

~2 min

Abstract Words

136

Citations

0

Abstract

We provide a proof that there exists a bijection between local unitary (LU) orbits of absolutely maximally entangled (AME) states in \(mathbb{C}D\)otimes n where n is even, also known as perfect tensors, and LU orbits of ((n-1,D,n/2))D quantum error correcting codes. Thus, by a result of Rather et al. (2023), the AME state of 4 qutrits and the pure ((3,3,2))3 qutrit code mathcal{C} are both unique up to the action of the LU group. We further explore the connection between the 4-qutrit AME state and the code mathcal{C} by showing that the group of transversal gates of mathcal{C} and the group of local symmetries of the AME state are closely related. Taking advantage of results from Vinberg's theory of graded Lie algebras, we find generators of both of these groups.

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  • We provide a proof that there exists a bijection between local unitary (LU) orbits of absolutely maximally entangled (AME) states in (mathbbC^D^otimes n) where n is even, also...

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References & Citation Signals

[1] DOI https://doi.org/arXiv:2601.19677 [2] arXiv https://arxiv.org/abs/2601.19677 [3] Publisher https://arxiv.org/abs/2601.19677

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External citation index: OpenAlex citation signal • updated 2026-06-11 18:30:06

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