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首页> 外文期刊>Journal of physics, A. Mathematical and theoretical >The non-disjoint ontic states of the Grassmann ontological model, transformation contextuality, and the single qubit stabilizer subtheory
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The non-disjoint ontic states of the Grassmann ontological model, transformation contextuality, and the single qubit stabilizer subtheory

机译：基层本体本体模型，转换语境和单个稳定器子理论的非脱节ontic状态

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摘要

We show that it is possible to construct a preparation non-contextual ontological model that does not exhibit 'transformation contextuality' for single qubits in the stabilizer subtheory. In particular, we consider the 'blowtorch' map and show that it does not exhibit transformation contextuality under the Grassmann Wigner-Weyl-Moyal (WWM) qubit formalism. Furthermore, the transformation in this formalism can be fully expressed at order (h) over bar (0), where it satisfies all of Kohnogorov's axioms of classical probability theory, and so does not qualify as a candidate quantum phenomenon. In particular, we find that the Grassmann WWM formalism at order (h) over bar (0) corresponds to an ontological model governed by an additional set of constraints arising from the relations defining the Grassmann algebra. Due to this additional set of constraints, the allowed probability distributions in this model do not form a single convex set when expressed in terms of disjoint ontic states and so cannot be mapped to models whose states form a single convex set over disjoint ontic states. However, expressing the Grassmann WWM ontological model in terms of non-disjoint ontic states corresponding to the monomials of the Grassmann algebra results in a single convex set. We further show that a recent result by Lillystone et al that proves a broad class of preparation and measurement non-contextual ontological models must exhibit transformation contextuality lacks the generality to include the ontological model considered here; Lillystone et al's result is appropriately limited to ontological models whose states produce a single convex set when expressed in terms of disjoint ontic states. Therefore, we prove that for the qubit stabilizer subtheory to be captured by a preparation, transformation and measurement non-contextual ontological theory, it must be expressed in terms of non-disjoint ontic states, unlike the case for the odd-dimensional single-qudit stabilizer subtheory.
机译：我们表明，可以构建一个制备非上下文本体主义模型，该模型不会在稳定器子理论中为单个Qubits表现出“转换语境”。特别是，我们考虑“吹风机”地图，并表明它在Grassmann Wigner-Weyl-Moyal（WWM）Qubit形式主义下没有表现出转换语境。此外，这种形式主义中的变换可以在杆（0）上以顺序（h）完全表达，其中满足古典概率理论的所有Kohnogorov的公理，因此不符合候选量子现象。特别是，我们发现，GARSMANN WWM形式主义（h）上方的条（0）对应于由定义Grassmann代数的关系产生的一系列内容限制的本体主义模型。由于该额外的约束集，当在不相交的Ontic状态时表达时，该模型中的允许概率分布不会形成单个凸面集，因此不能映射到状态形成在不相交的ontic状态上的单个凸起的模型。然而，在对应于基于Grassmann代数的单体的非脱节ontic状态方面表达了基层WWM本体模型，导致单个凸起。我们进一步表明，Lillystone等的最近结果证明了广泛的准备和测量非语境本体本体模型必须表现出转化语境，缺乏包括在此考虑的本体论模型的普遍性; Lillystone等人的结果适当地限于在不相交的Ontic状态表达时产生单个凸面集的本体模型。因此，我们证明，对于按准备，转换和测量非语境本体理论捕获的Qubit稳定剂亚文体，它必须以非不相交的ontic状态表达，而不是奇数单Qudit的情况。稳定剂亚文学。

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