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High-dimensional quantum communication complexity beyond strategies based on Bell's theorem
Physical Review Letters ( IF 8.6 ) Pub Date : 
Daniel Martínez, Armin Tavakoli, Mauricio Casanova, Gustavo Cañas, Breno Marques, and Gustavo Lima

Quantum resources can improve communication complexity problems (CCPs) beyond their classical constraints. One quantum approach is to share entanglement and create correlations violating a Bell inequality, which can then assist classical communication. A second approach is to resort solely to the preparation, transmission and measurement of a single quantum system; in other words quantum communication. Here, we show the advantages of the latter over the former in high-dimensional Hilbert space. We focus on a family of CCPs, based on facet Bell inequalities, study the advantage of high-dimensional quantum communication, and realise such quantum communication strategies using up to ten-dimensional systems. The experiment demonstrates, for growing dimension, an increasing advantage over quantum strategies based on Bell inequality violation. For sufficiently high dimensions, quantum communication also surpasses the limitations of the post-quantum Bell correlations obeying only locality in the macroscopic limit. We find that the advantages are tied to the use of measurements that are not rank-one projective, and provide an experimental semi-device-independent falsification of such measurements in Hilbert space dimension six.

中文翻译:

高维量子通信复杂性超越了基于贝尔定理的策略

量子资源可以改善通信复杂性问题(CCP),超越其传统的限制。一种量子方法是共享纠缠并创建违反贝尔不等式的相关性,然后可以协助经典通信。第二种方法是仅求助于单个量子系统的准备,传输和测量。换句话说,量子通信。在这里,我们展示了后者在高维希尔伯特空间中相对于前者的优势。我们关注基于面贝尔不等式的CCP系列,研究高维量子通信的优势,并使用多达十维的系统来实现这种量子通信策略。该实验表明,对于不断扩大的规模,它比基于Bell不等式违背的量子策略具有越来越大的优势。对于足够高的尺寸,量子通信还超越了量子后贝尔相关性的局限性,仅遵守了宏观极限中的局部性。我们发现,这些优势与使用非一等投射的测量方法有关,并在希尔伯特空间维数为6的实验中提供了一种与实验无关的与半设备无关的伪造方法。
更新日期:2018-09-18
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