Tavakoli Armin, Farkas Máté, Rosset Denis, Bancal Jean-Daniel, Kaniewski Jedrzej
Department of Applied Physics, University of Geneva, 1211 Geneva, Switzerland.
Institute of Theoretical Physics and Astrophysics, National Quantum Information Centre, Faculty of Mathematics, Physics and Informatics, University of Gdansk, 80-952 Gdansk, Poland.
Sci Adv. 2021 Feb 10;7(7). doi: 10.1126/sciadv.abc3847. Print 2021 Feb.
Mutually unbiased bases (MUBs) and symmetric informationally complete projectors (SICs) are crucial to many conceptual and practical aspects of quantum theory. Here, we develop their role in quantum nonlocality by (i) introducing families of Bell inequalities that are maximally violated by -dimensional MUBs and SICs, respectively, (ii) proving device-independent certification of natural operational notions of MUBs and SICs, and (iii) using MUBs and SICs to develop optimal-rate and nearly optimal-rate protocols for device-independent quantum key distribution and device-independent quantum random number generation, respectively. Moreover, we also present the first example of an extremal point of the quantum set of correlations that admits physically inequivalent quantum realizations. Our results elaborately demonstrate the foundational and practical relevance of the two most important discrete Hilbert space structures to the field of quantum nonlocality.
相互无偏基（MUBs）和对称信息完备投影算子（SICs）对于量子理论的许多概念和实际方面都至关重要。在此，我们通过以下方式阐述它们在量子非局域性中的作用：（i）引入分别被(d)维MUBs和SICs最大程度违背的贝尔不等式族；（ii）证明MUBs和SICs自然操作概念的与设备无关的认证；（iii）分别使用MUBs和SICs为与设备无关的量子密钥分发和与设备无关的量子随机数生成开发最优速率和近最优速率协议。此外，我们还给出了量子关联集的一个极值点的首个示例，该极值点允许物理上不等价的量子实现。我们的结果精心展示了两种最重要的离散希尔伯特空间结构对量子非局域性领域的基础和实际相关性。
