The original quantum discord (QD) is shown to be not monogamous except for the three-qubit states. Recently, a complete monogamy relation for multiparty quantum system was established for entanglement in (Guo and Zhang 2020 Phys. Rev. A 101 032301), and in addition, a new multipartite generalization of QD was proposed in (Radhakrishnan et al 2020 Phys. Rev. Lett. 124 110401). In this work, we firstly define the complete monogamy for this multipartite quantum discord (MQD) and the global quantum discord (GQD). MQD, with the same spirit as the complete monogamy of entanglement, is said to be completely monogamous (i) if it does not increase under coarsening of subsystems and (ii) if some given combination of subsystems reach the total amount of the correlation, then all other combination of subsystems that do not include all the given subsystems do not contain such a correlation any more. Here, coarsening of subsystems means discarding or combining some subsystems up to the given partition. Simultaneously, the complete monogamy of GQD is also defined with slight modification on the coarsening relation. Consequently, we explore all the coarsening relations of MQD and show that it is completely monogamous with a modicum assumption. In addition, with the same spirit, we investigate all the coarsening relations for GQD and show that GQD is not completely monogamous. That is, in the sense of the complete monogamy relation, MQD as a generalization of the original QD captures the nature of such a quantum correlation, and thus it is nicer than GQD as a generalization.

除了三量子位状态外，原始的量子不和谐 (QD) 被证明不是一夫一妻制的。最近，在（Guo and Zhang 2020 Phys. Rev. A 101 032301）中建立了多方量子系统的完全一夫一妻制关系，此外，在（Radhakrishnan et al 2020 Phys. Rev. A 101 032301）中提出了一种新的QD多方推广. 让. 124110401）。在这项工作中，我们首先为这种多方量子不和谐（MQD）和全球量子不和谐（GQD）定义了完全一夫一妻制。MQD 与纠缠的完全一夫一妻制具有相同的精神，被称为完全一夫一妻制（i）如果它在子系统粗化下不增加，以及（ii）如果某个给定的子系统组合达到相关性的总量，则不包括所有给定子系统的所有其他子系统组合不再包含这种相关性。在这里，子系统的粗化意味着丢弃或组合一些子系统直到给定的分区。同时，GQD 的完全一夫一妻制也被定义为对粗化关系稍作修改。最后，我们探索了 MQD 的所有粗化关系，并表明它是完全一夫一妻制的，带有一点点假设。此外，本着同样的精神，我们研究了 GQD 的所有粗化关系，并表明 GQD 不是完全一夫一妻制的。也就是说，在完全一夫一妻制的意义上，MQD 作为原始 QD 的推广抓住了这种量子关联的性质，因此它比 GQD 作为推广更好。