= Distance of a quantum error-correcting code
{title2=$[[n,k,d]]$}
= Quantum code distance
{synonym}
An $[[n,k,d]]$ <quantum error correction> code is a $2^k$-dimensional subspace of $n$ <qubits>. Its distance $d$ is the minimum weight of a <Pauli operator> $E$ for which $PEP$ is not a scalar multiple of the code projector $P$. Thus every operator supported on fewer than $d$ qubits has scalar compression to the code, by expansion in the Pauli basis. This definition includes degenerate codes; a low-weight operator acting as a scalar does not reduce the distance.
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