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Newly, during an analytical calculation M. A. Yurischev [arXiv: 1302.5239 (2013)] prove that quantum discord (or entanglement) remains unchangeable for any centrosymmetric (CS) states that are converted to their corresponding mode X. In this paper, in addition to the above calculations, the conditions which geometric measure remains constant are presented. This work will be completed with discussion about two physical examples.

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