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Not-Post-Peierls compatibility under noisy channels

机译：在嘈杂的频道下的非Peierls兼容性

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The Pusey-Barrett-Rudolph (PBR) theorem deals with the realism of the quantum states. It establishes that every pure quantum state is real, in the context of quantum ontological models. Specifically, by guaranteeing the property of not-Post-Peierls ((sic) PP) compatibility (or antidistinguishability) for a particular set of states P, together with the ad hoc postulate known as preparation independence postulate (PIP), the theorem establishes that these two properties imply the Psi-onticity (realism) of the set of all pure states. This PBR result has triggered two particular lines of research: On the one hand, it has been possible to derive similar results without the use of the PIP, although at the expense of implying weaker properties than Psi-onticity. On the other hand, it has also been proven that the property of (sic) PP compatibility alone is an explicit witness of usefulness for the task known as conclusive exclusion of states. In this work, we explore the (sic) PP compatibility of the set of states P, when P is under the interaction of some noisy channels, which would consequently let us identify some noisy scenarios where it is still possible to perform the task of conclusive exclusion of states. Specifically, we consider the set P of n-qubit states in interaction with an environment by means of (i) individual and (ii) collective couplings. In both cases, we analytically show that the phenomenon of achieving (sic) PP compatibility, although reduced, it is still present. Searching for an optimisation of this phenomenon, we report numerical experiments up to n = 4 qubits. For individual qubit-noise coupling, be it a bit, a phase, or a bit-phase flip noise, the numerical search exhibits the same response to all the different noisy channels, without improving the analytical expectation. In contrast, the collective qubit-noise coupling leads to a more efficient numerical display of the phenomenon, and a variety of noise channel-dependent behaviours emerge. Furthermore, by adopting a slight modification of the definition of Psi-onticity, from being a property exclusively of sets of pure states to be a property of general sets of states (now rho-onticity), in particular of the considered noisy set P, our results can also be seen as addressing the rho-ontic realism of the set of n-qubit states P under the considered noisy channels.
机译：Pusey-Barrett-Rudolph（PBR）定理涉及量子州的现实主义。在量子本体本体模型的背景下，建立了每个纯量子状态是真实的。具体而具体地，通过保证特定状态集合的非Peierls（（SiC）PP）兼容性（或反歧隐含性）的性质，与被称为制备独立假设（PIP）的特设假设一起，定理建立该兼容性这两个属性意味着所有纯粹状态集的PSI-OnTicity（现实主义）。该PBR结果已触发两条特定的研究线：一方面，在不使用PIP的情况下，可以获得类似的结果，尽管以暗示比PSI-Ontiity的特性为代价。另一方面，还证明了（SIC）PP兼容性的财产仅仅是明确的证人对被称为国家的结论的任务的有用性。在这项工作中，我们探讨了该集合P集的（SIC）PP兼容性，当P是一些嘈杂的频道的互动时，这将让我们识别一些嘈杂的情景，在那里仍然可以执行决定性的任务排除国家。具体地，我们考虑通过（i）个体和（ii）集体耦合的与环境相互作用的N-QUBET状态的集合P.在这两种情况下，我们分析表明，实现了（SIC）PP兼容性的现象，但仍然减少，仍然存在。搜索优化这种现象，我们向N = 4 QUBits报告数值实验。对于单个QUBbit-噪声耦合，可以是一位，相位或位相翻转噪声，数值搜索表现出对所有不同噪声通道的相同响应，而不会提高分析期望。相反，集体qubit噪声耦合导致更有效的现象数值显示，并且出现了各种噪声通道的行为。此外，通过采用PSI-Ontifity的定义轻微修改，从作为一套纯粹状态的属性是常规（现在Rho-Ontiity）的一般组，特别是考虑的嘈杂集P，我们的结果也可以在考虑的嘈杂渠道下寻求讲述N-Qubit状态P集的Rho-Ontic现实主义。

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