Tight upper bound of the maximal quantum violation of Gisin’s elegant Bell inequality and its application in randomness certification

IF 5.8 2区 物理与天体物理 Q1 OPTICS
Dan-Dan Hu, Meng-Yan Li, Fen-Zhuo Guo, Yu-Kun Wang, Hai-Feng Dong, Fei Gao
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Abstract

The violation of a Bell inequality implies the existence of nonlocality, making device-independent randomness certification possible. This paper derives a tight upper bound for the maximal quantum violation of Gisin’s elegant Bell inequality (EBI) for arbitrary two-qubit states, along with the constraints required to achieve this bound. This method provides the necessary and sufficient conditions for violating the EBI for several quantum states, including pure two-qubit states and the Werner states. The lower bound of certifiable global randomness is analyzed based on the tight upper bound of the EBI for pure two-qubit states, with a comparison to the Clauser-Horne-Shimony-Holt (CHSH) inequality. The relationship between the noise level and the lower bound of certifiable global randomness with respect to the Werner states is also explored, and the comparisons with both the CHSH inequality and the chained inequality are given. The results indicate that when the state approaches a maximally entangled state within specific quantified ranges, the EBI demonstrates advantages over both the CHSH inequality and the chained inequality, providing theoretical guidance for experimental device-independent quantum random number generation.

Gisin优雅贝尔不等式最大量子违反的紧上界及其在随机性证明中的应用
贝尔不等式的违反意味着非定域性的存在,使得与设备无关的随机性认证成为可能。本文推导了任意二量子位态Gisin优雅贝尔不等式(EBI)的最大量子违逆的紧上界,以及实现该边界所需的约束条件。该方法为纯双量子位态和Werner态等几种量子态违反EBI提供了充分必要条件。基于纯二量子位态EBI的紧上界,分析了可认证全局随机性的下界,并与clauser - horn - shimony - holt (CHSH)不等式进行了比较。讨论了噪声水平与可证明全局随机的Werner状态下界的关系,并与CHSH不等式和链式不等式进行了比较。结果表明,当态在特定的量化范围内接近最大纠缠态时,EBI优于CHSH不等式和链式不等式,为实验设备无关的量子随机数生成提供了理论指导。
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来源期刊
EPJ Quantum Technology
EPJ Quantum Technology Physics and Astronomy-Atomic and Molecular Physics, and Optics
CiteScore
7.70
自引率
7.50%
发文量
28
审稿时长
71 days
期刊介绍: Driven by advances in technology and experimental capability, the last decade has seen the emergence of quantum technology: a new praxis for controlling the quantum world. It is now possible to engineer complex, multi-component systems that merge the once distinct fields of quantum optics and condensed matter physics. EPJ Quantum Technology covers theoretical and experimental advances in subjects including but not limited to the following: Quantum measurement, metrology and lithography Quantum complex systems, networks and cellular automata Quantum electromechanical systems Quantum optomechanical systems Quantum machines, engineering and nanorobotics Quantum control theory Quantum information, communication and computation Quantum thermodynamics Quantum metamaterials The effect of Casimir forces on micro- and nano-electromechanical systems Quantum biology Quantum sensing Hybrid quantum systems Quantum simulations.
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