We relate the phenomenon of local indistinguishability of orthogonal states with the properties of unextendibility and uncompletability of entangled bases for bipartite and multipartite quantum systems. We prove that all two-qubit unextendible entangled bases are of size three and they cannot be perfectly distinguished by separable measurements. We identify a method of constructing two-element orthogonal ensembles, based on the concept of unextendible entangled bases, that can potentially lead to information sharing applications. Two-element ensembles form the fundamental unit of ensembles, and yet does not offer locally indistinguishable ensembles for pure state elements. Going over to mixed states does open this possibility, but can be difficult to identify. The method provided using unextendible entangled bases can be used for their systematic generation. In multipartite systems, we find a class of unextendible entangled bases for which the unextendibility property remains conserved across all bipartitions. We also identify nonlocal operations, local implementation of which require entangled resource states from a higher-dimensional quantum system.

我们将正交态的局部不可区分现象与二分和多分量子系统的纠缠基的不可扩展性和不可完成性联系起来。我们证明所有两个量子比特不可扩展的纠缠碱基的大小都是 3，并且无法通过可分离的测量来完全区分。我们基于不可扩展纠缠基的概念，确定了一种构造二元正交系综的方法，该方法可能会导致信息共享应用。二元素系综构成了系综的基本单位，但并不为纯态元素提供局部不可区分的系综。转到混合状态确实打开了这种可能性，但可能难以识别。使用不可扩展的纠缠碱基提供的方法可用于它们的系统生成。在多分系统中，我们发现了一类不可扩展的纠缠基，其不可扩展性在所有二分系统中都保持保守。我们还确定了非本地操作，其本地实现需要来自更高维量子系统的纠缠资源状态。