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arXiv 1503.05936quant-ph
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后选择是物理的吗:一个设备独立的展望

Is Post Selection Physical: A Device Independent Outlook

Anubhav Chaturvedi, Tushant Jha, Indranil Chakrabarty

摘要:

这项工作背后的基本动机是提出一个问题,即职位选择是否可以被认为是一个有效的物理转换(概率空间)或没有。我们研究的后果,这两个答案设置在一个设备(理论)独立的框架,只根据观察到的统计数据。我们首先将后选择作为一个假设,并使用由布尔函数控制的独立设备进行建模。我们建立类比后选择函数和一般的概率博弈中的两方二进制输入输出的情况。作为观察,我们根据对均匀输入概率分布的影响对所有可能的后选择函数进行分类。我们发现后选择可以将简单的无信号概率分布转换为信号。类似地,解决NP完全问题很容易独立于经典或量子计算(特别是我们证明后RP = NP)。最后,我们展示了一个独立于基本理论的鸽子洞原则的违反的例子。作为我们的理论独立建模的结果,我们得出结论,后选择作为一个假设增加了权力的基础理论。特别是,量子力学受益于后选择假设,只是因为它承认一个更一般的允许概率集相比,本地隐藏变量模型。在没有假设的情况下,我们关联了一个与设备无关的效率因子来量化职位选择的成本。我们的研究表明,在现实世界中,后选择的效率不足以成为任何优势。但从对抗的角度来看,它仍然具有重要意义。作为一个应用程序,我们得到了强大的边界伪造的钟违反最低效率方面所需的使用后选择。

英文摘要:

The basic motivation behind this work is to raise the question that whether post selection can be considered a valid physical transformation (on probability space) or not. We study the consequences of both answers set in a device (theory) independent framework, based only on observed statistics. We start with taking up post-selection as an assumption and model the same using independent devices governed by Boolean functions. We establish analogy between the post selection functions and the general probabilistic games in a two party binary input-output scenario. As an observation, we categorize all possible post-selection functions based on the effect on a uniform input probability distribution. We find that post-selection can transform simple no signaling probability distributions to signaling. Similarly, solving NP complete problems is easy independent of classical or quantum computation (in particular we prove that Post RP = NP). Finally, we demonstrate an instance of the violation of the pigeon hole principle independent of underlying theory. As result of our theory independent modeling we conclude that post-selection as an assumption adds power to the underlying theory. In particular, quantum mechanics benefits more with the post-selection assumption, only because it admits a more general set of allowed probabilities as compared to the local hidden variable model. Without the assumption we associate a device independent efficiency factor to quantify the cost of post selection. Our study shows that in the real world post-selection is not efficient enough to be of any advantage. But from an adversarial perspective it is still of significance. As an application, we obtain robust bounds on faking the bell violation in terms of minimum efficiency required using post selection.

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