Correlations in multiparticle systems are constrained by restrictions from quantum mechanics. A prominent example for these restrictions are monogamy relations, limiting the amount of entanglement between pairs of particles in a three-particle system. A powerful tool to study correlation constraints is the notion of sector lengths. These quantify, for different k , the amount of k -partite correlations in a quantum state in a basis-independent manner. We derive tight bounds on the sector lengths in multi-qubit states and highlight applications of these bounds to entanglement detection, monogamy relations and the n -representability problem. For the case of two- and three qubits we characterize the possible sector lengths completely and prove a symmetrized version of strong subadditivity for the linear entropy.

中文翻译：

---

通过扇区长度表征量子态

多粒子系统中的相关性受到量子力学的限制。这些限制的一个突出例子是一夫一妻制关系，它限制了三粒子系统中成对粒子之间的纠缠量。研究关联约束的强大工具是扇区长度的概念。这些针对不同的k以与基无关的方式量化了处于量子态的k部分相关量。我们推导了多量子位状态中扇区长度的严格边界，并重点说明了这些边界在纠缠检测，一夫一妻制关系和n-可表示性问题中的应用。对于两个和三个量子位，我们完全刻画了可能的扇区长度，并证明了线性熵的强次可加性的对称形式。