We address the problem of compressing density operators defined on a finite dimensional Hilbert space which assumes a tensor product decomposition. In particular, we look for an efficient procedure for learning the most likely density operator, according to ‘Jaynes’ principle, given a chosen set of partial information obtained from the unknown quantum system we wish to describe. For complexity reasons, we restrict our analysis to tree-structured sets of bipartite marginals. We focus on the tripartite scenario, where we solve the problem for the couples of measured marginals which are compatible with a quantum Markov chain, providing then an algebraic necessary and sufficient condition for the compatibility to be verified. We introduce the generalization of the procedure to the n-partite scenario, giving some preliminary results. In particular, we prove that if the pairwise Markov condition holds between the subparts then the choice of the best ...

中文翻译：

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直接量子相关性的可回收性

我们解决了压缩假设在张量积分解的有限维希尔伯特空间上定义的密度算符的问题。尤其是，考虑到从我们要描述的未知量子系统中获得的部分选择信息，我们根据“ Jaynes”原理寻找一种有效的方法来学习最可能的密度算子。出于复杂性原因，我们将分析限制在二叉边际树形结构集上。我们专注于三方场景，在该场景中，我们解决了与量子马尔可夫链兼容的被测边缘对的问题，然后提供了代数的必要性和充分条件来验证兼容性。我们将程序推广到n部分场景，给出一些初步结果。尤其是，