Shahrood University of TechnologyJournal of Algebraic Systems2345-51283120150601GENERALIZED JOINT HIGHER-RANK NUMERICAL RANGE313848610.22044/jas.2015.486ENH. R. AfshinDepartment of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran.S. BagheriDepartment of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran.M. A. MehrjoofardDepartment of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran.Journal Article20150116The 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.https://jas.shahroodut.ac.ir/article_486_30a2c8fdb2eec77f2ced44e835d901de.pdf