Abstract
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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