论文标题
尺寸见证的图理论方法
Graph-theoretic approach to dimension witnessing
论文作者
论文摘要
量子计算和量子信息中的一个基本问题是找到任务所需的最小量子维度。对于涉及状态准备和测量的任务，只能使用输入输出相关性解决此问题。这已应用于贝尔，准备和衡量以及科钦 - 塞普克上下文情景。在这里，我们介绍了一种新颖的方法，可以通过一项制剂和几个测量结果来见证场景的量子维度，该方法使用了一组测量事件之间的相互排他性图。我们介绍了图形理论量子维度所需的概念和工具，并通过识别新颖的量子维度证人来说明它们的使用，包括一个可以在很少有事件的情况下证明任意高量子维度的家庭。
A fundamental problem in quantum computation and quantum information is finding the minimum quantum dimension needed for a task. For tasks involving state preparation and measurements, this problem can be addressed using only the input-output correlations. This has been applied to Bell, prepare-and-measure, and Kochen-Specker contextuality scenarios. Here, we introduce a novel approach to quantum dimension witnessing for scenarios with one preparation and several measurements, which uses the graphs of mutual exclusivity between sets of measurement events. We present the concepts and tools needed for graph-theoretic quantum dimension witnessing and illustrate their use by identifying novel quantum dimension witnesses, including a family that can certify arbitrarily high quantum dimensions with few events.
