# Illustration Phase Flip Error in a Kitaev Chain

Get illustration

Share — copy and redistribute the material in any medium or format

Adapt — remix, transform, and build upon the material for any purpose, even commercially.

Sharing and adapting of the illustration is allowed with indication of the link to the illustration.

In a Kitaev chain, a phase error $$\sigma^{\mathrm z}_j$$ can occur where one state $$|1\rangle$$ changes sign while $$|0\rangle$$ relative to it does not:\begin{align} \sigma^{\mathrm z}_j \, |0\rangle ~&=~ |0\rangle \\ \sigma^{\mathrm z}_j \, |1\rangle ~&=~ -|1\rangle \end{align}

The phase flip error is represented by the Pauli-Z matrix $$\sigma^{\mathrm z}_j$$, even if the Kitaev chain is not a spin system. According to the Wigner-Jordan transformation, a spin system is equivalent to a fermionic system (particle / no particle) like the Kitaev chain.