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For a noisy quantum channel, a quantum error correction code of dimension k exists if and only if the joint rank- numerical range associated with the error operators of the channel is non-empty. In this paper, the joint rank-
numerical range of an
-tuple of elements in the
-qubit Pauli group are discussed. Let
be a Hermitian triple in the
-qubit Pauli group. We state a constructive method to obtain the joint rank-
numerical range of
. Moreover, we show that
.
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