arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2007.10746quant-phcs.DM
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尺寸证明的图论方法

Graph-theoretic approach to dimension witnessing

Maharshi Ray, Naresh Goud Boddu, Kishor Bharti, Leong-Chuan Kwek, Adán Cabello

摘要:

在量子计算和量子信息中的一个基本问题是寻找一个任务所需的最小量子维数。对于涉及状态准备和测量的任务,可以仅使用输入-输出相关性来解决该问题。这已被应用到贝尔,测量和测量,和Kochen-Specker情境场景。在这里,我们介绍了一种新的方法,量子维见证的情况下,一个准备和几个测量,它使用的图形之间的互斥测量事件集。我们提出的概念和工具需要图论量子维见证,并说明其使用识别新的量子维证人,包括一个家庭,可以证明任意高的量子尺寸与几个事件。

英文摘要:

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.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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