arXiv 1402.57222014-02-24quant-ph

来自有效反扩散剂的熵不确定性

Entropic uncertainty from effective anti-commutators

Jędrzej Kaniewski, Marco Tomamichel, Stephanie Wehner

备注：: 5 pages, 3 figures (excluding Supplemental Material), revtex
发表信息：: Phys. Rev. A 90, 012332 (2014)
DOI：: 10.1103/PhysRevA.90.012332

摘要：

我们研究两个或多个二元测量的熵不确定性关系，例如自旋- $\frac{1}{2}$或偏振测量。我们认为，这些测量的有效的反干扰因子，即在测量之前对状态进行评估的反干扰因子，是测量不相容性的一种权宜之计。基于两两有效反算子的知识，我们导出了一类以条件Rényi熵表示的熵测不准关系。我们的不确定性关系制定的有效措施的不兼容性，这可以独立于设备进行认证。因此，我们讨论了我们的研究结果的潜在应用设备无关的量子密码学。此外，为了研究我们的分析的紧密性，我们考虑了最简单的（并且非常好研究的）量子比特上的两个测量的场景。我们发现，我们的结果优于著名的约束，由于Maassen和Uffink [物理学。60，1103（1988）]，并提供了一个新的分析表达式的最小不确定性，也优于最近的一些界限的基础上优化。

英文摘要：

We investigate entropic uncertainty relations for two or more binary measurements, for example spin-$\frac{1}{2}$ or polarisation measurements. We argue that the effective anti-commutators of these measurements, i.e. the anti-commutators evaluated on the state prior to measuring, are an expedient measure of measurement incompatibility. Based on the knowledge of pairwise effective anti-commutators we derive a class of entropic uncertainty relations in terms of conditional Rényi entropies. Our uncertainty relations are formulated in terms of effective measures of incompatibility, which can be certified device-independently. Consequently, we discuss potential applications of our findings to device-independent quantum cryptography. Moreover, to investigate the tightness of our analysis we consider the simplest (and very well-studied) scenario of two measurements on a qubit. We find that our results outperform the celebrated bound due to Maassen and Uffink [Phys. Rev. Lett. 60, 1103 (1988)] and provide a new analytical expression for the minimum uncertainty which also outperforms some recent bounds based on majorisation.

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