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valbert4 committed Jan 21, 2025
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The sets of \(GF(q^2)\)-represented vectors for all generators yield a trace-alternating self-orthogonal additive code over \(GF(q^2)\).
Recalling that \(q=p^m\), Galois-qudit stabilizer codes can also be treated as prime-qudit stabilizer codes on \(mn\) qudits, giving \(k=nm-r\) \cite{doi:10.1109/18.959288}.
As such, modular-qudit stabilizer states can be expressed in terms of linear and quadratic functions over \(\mathbb{Z}_p^{mn\) \cite{arxiv:quant-ph/0408190}.
As such, modular-qudit stabilizer states can be expressed in terms of linear and quadratic functions over \(\mathbb{Z}_p^{mn}\) \cite{arxiv:quant-ph/0408190}.
Such states correspond to the set of states with positive Wigner functions \cite{arxiv:quant-ph/0602001,arxiv:quant-ph/0702004}.
Galois-qudit stabilizer codes can equivalently \cite{arxiv:quant-ph/0111080} (see also \cite{arxiv:quant-ph/0308151,arxiv:quant-ph/0703112}) be defined using graphs, yielding an analytical form for the codewords \cite{arxiv:quant-ph/0012111}.
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