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Article

generalized joint higher-rank numerical range

m. a. mehrjoofard, h. r. afshin, s. bagheri

Abstract

the rank-k numerical range has a close connection to the construction of quantum error correction code for a noisy quantum channel. for noisy quantum channel, a quantum error correcting code of dimension k exists if and only if the associated joint rank-k numerical range is non-empty. in this paper the notion of joint rank-k numerical range is generalized and some statements of [2011, generalized numerical ranges and quantum error correction, j. operator theory, 66: 2, 335-351.] are extended.

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