A note on codes and kets
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 2 (2005), pp. 79-82
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To every binary linear $[n,k]$ code $C$ we associate a quantum state $|\Psi_C\rangle\in H^{\otimes n}$, where $H$ is the two-dimensional complex Hilbert space associated to the spin $\frac12$ particle. For the state $|\Psi_C\rangle$ we completely characterize all the expectation values of the products of spins measured, for each one out of the $n$ particles, either in the $x$- or in the $y$-direction. This establishes an interesting relationship with the dual code $C^{\perp}$.
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