Spin code 

Root code for the Spin Kingdom

Description

Encodes \(K\)-dimensional Hilbert space into a tensor-product or direct sum of factors, with each factor spanned by states of a quantum mechanical spin or, more generally, an irreducible representation of a Lie group.

In the simplest case of a spin, the canonical states \(|^J_m\rangle\) of a single \(2J+1\)-dimensional factor are labeled by total angular momentum \(J\) (either integer or half-integer) and its \(z\)-axis projection \(m\). There can be multiple factors of the same size, as in the case of atomic or molecular state spaces, and the number of factors can be infinite. In contrast to other qudit codes, spin codes are closely associated with the angular momentum Lie algebra and/or the Lie groups \(SU(2)\) or \(SO(3)\).

Protection

Some spin codes are designed to protect against \(SU(2)\) rotations by small angles, while others protect against changes in the total angular momentum \(J\) or its projection \(m\).

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Zoo Code ID: spins_into_spins

Cite as:
“Spin code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/spins_into_spins
BibTeX:
@incollection{eczoo_spins_into_spins, title={Spin code}, booktitle={The Error Correction Zoo}, year={2022}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/spins_into_spins} }
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Permanent link:
https://errorcorrectionzoo.org/c/spins_into_spins

Cite as:

“Spin code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/spins_into_spins

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/spins/spins_into_spins.yml.