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arXiv 1802.06121quant-ph
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上下文和单量子比特稳定子形式主义

Contextuality and The Single-Qubit Stabilizer Formalism

Piers Lillystone, Joel J. Wallman, Joseph Emerson

备注：
5 pages, 1 figure
发表信息：
Phys. Rev. Lett. 122, 140405 (2019)
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摘要：

背景性是量子理论的一个基本的非经典性质，最近被证明是在一些领先的量子计算模型中实现量子加速的关键资源。然而，在量子计算的任意模型中，需要哪种形式的上下文性，以及需要多少上下文性来获得加速，仍然不清楚。在本文中，我们表明，上下文和计算优势之间的关系比以前认为的更复杂。我们实现这一点，通过证明广义的上下文是存在的，即使在最简单的量子操作的子集，所谓的单量子比特稳定器理论，它没有提供计算的优势，以前被认为是完全非上下文。然而，单量子比特稳定器理论的上下文性可以被限制在变换中。因此，我们的结果也表明，通常考虑的测量和测量方案（忽略变换）没有完全捕捉到量子理论的上下文。

英文摘要：

Contextuality is a fundamental non-classical property of quantum theory, which has recently been proven to be a key resource for achieving quantum speed-ups in some leading models of quantum computation. However, which of the forms of contextuality, and how much thereof, are required to obtain a speed-up in an arbitrary model of quantum computation remains unclear. In this paper, we show that the relation between contextuality and a compuational advantage is more complicated than previously thought. We achieve this by proving that generalized contextuality is present even within the simplest subset of quantum operations, the so-called single-qubit stabilizer theory, which offers no computational advantage and was previously believed to be completely non-contextual. However, the contextuality of the single-qubit stabilizer theory can be confined to transformations. Therefore our result also demonstrates that the commonly considered prepare-and-measure scenarios (which ignore transformations) do not fully capture the contextuality of quantum theory.

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