Unlike quantum correlations, the shareability of classical correlations (CCs) between two parties of a multipartite state is assumed to be free since there exist states for which CCs for each of the reduced states can simultaneously reach their algebraic maximum value. However, when one randomly picks out states from the state space, we find that the probability of obtaining those states possessing the algebraic maximum value is vanishingly small. Therefore, the possibility of a nontrivial upper bound on the distribution of CCs that is less than the algebraic maxima emerges. We explore this possibility by Haar uniformly generating random multipartite states and computing the frequency distribution for various CC measures, conventional classical correlators, and two axiomatic measures of classical correlations, namely, the classical part of quantum discord and local work of work-deficit. We find that the distributions are typically Gaussian-like and their standard deviations decrease with the increase in number of parties. It also reveals that, among the multiqubit random states, most of the reduced density matrices possess a low amount of CCs which can also be confirmed by the mean of the distributions, thereby showing a kind of restrictions on the shareability of classical correlations for random states. Furthermore, we also notice that the maximal value for random states is much lower than the algebraic maxima obtained for a set of states, and the gap between the two increases further for states with a higher number of parties. We report that, for a higher number of parties, the classical part of quantum discord and local work can follow a monogamy-based upper bound on shareability while classical correlators have a different upper bound. The trends of shareability for classical correlation measures in random states clearly demarcate between the axiomatic definition of classical correlations and the conventional ones.

中文翻译：

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随机多部分量子态经典相关性的可共享性限制

与量子相关性不同，多部分状态的两方之间的经典相关性（CC）的可共享性假定为自由，因为存在一些状态，其中每个简化状态的CC可以同时达到其代数最大值。但是，当人们从状态空间中随机选择状态时，我们发现获得具有代数最大值的状态的可能性几乎很小。因此，出现了CC的分布上具有不重要的上限的可能性，该上限小于代数最大值。我们通过Haar均匀地生成随机多部分状态并计算各种CC测度，常规经典相关器和两个经典相关性的公理测度的频率分布，来探索这种可能性。量子不和谐的经典部分和局部工作不足。我们发现，分布通常呈高斯型，并且其标准偏差随参与方数量的增加而减小。它也表明，在多量子位随机状态中，大多数降密度矩阵具有少量的CC，这也可以通过分布的平均值来确认，从而显示出对随机状态经典相关性的可共享性的一种限制。 。此外，我们还注意到，随机状态的最大值远低于针对一组状态获得的代数最大值，并且对于方数较多的状态，两者之间的差距进一步增大。我们报告说，对于更多的缔约方，量子不和谐和局部工作的经典部分可以遵循基于一夫一妻制的可共享性上限，而经典相关器则具有不同的上限。随机状态下经典相关度量的可共享性趋势清楚地在经典相关的公理定义和常规相关之间进行了界定。