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• Photonics Research
• Vol. 10, Issue 7, 1582 (2022)
Wen-Rong Qi1、2、†, Jie Zhou3、†, Ling-Jun Kong4、5、†, Zhen-Peng Xu6, Hui-Xian Meng3, Rui Liu1, Zhou-Xiang Wang1, Chenghou Tu1, Yongnan Li1、8、*, Adán Cabello7, Jing-Ling Chen3、9、*, and Hui-Tian Wang4、10、*
Author Affiliations
• 1Key Laboratory of Weak-Light Nonlinear Photonics and School of Physics, Nankai University, Tianjin 300071, China
• 2School of Physics, Henan Normal University, Xinxiang 453007, China
• 3Theoretical Physics Division, Chern Institute of Mathematics, Nankai University, Tianjin 300071, China
• 4National Laboratory of Solid State Microstructures, Nanjing University, Nanjing 210093, China
• 5Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China
• 6Naturwissenschaftlich-Technische Fakultät, Universität Siegen, 57068 Siegen, Germany
• 7Departamento de Física Aplicada II, Universidad de Sevilla, E-41012 Sevilla, Spain
• 8e-mail: liyongnan@nankai.edu.cn
• 9e-mail: chenjl@nankai.edu.cn
• 10e-mail: htwang@nju.edu.cn
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Wen-Rong Qi, Jie Zhou, Ling-Jun Kong, Zhen-Peng Xu, Hui-Xian Meng, Rui Liu, Zhou-Xiang Wang, Chenghou Tu, Yongnan Li, Adán Cabello, Jing-Ling Chen, Hui-Tian Wang. Stronger Hardy-like proof of quantum contextuality[J]. Photonics Research, 2022, 10(7): 1582 Copy Citation Text show less

Abstract

A Hardy-like proof of quantum contextuality is a compelling way to see the conflict between quantum theory and noncontextual hidden variables (NCHVs), as the latter predict that a particular probability must be zero, while quantum theory predicts a nonzero value. For the existing Hardy-like proofs, the success probability tends to 1/2 when the number of measurement settings $n$ goes to infinity. It means the conflict between the existing Hardy-like proof and NCHV theory is weak, which is not conducive to experimental observation. Here we advance the study of a stronger Hardy-like proof of quantum contextuality, whose success probability is always higher than the previous ones generated from a certain $n$-cycle graph. Furthermore, the success probability tends to 1 when $n$ goes to infinity. We perform the experimental test of the Hardy-like proof in the simplest case of $n=7$ by using a four-dimensional quantum system encoded in the polarization and orbital angular momentum of single photons. The experimental result agrees with the theoretical prediction within experimental errors. In addition, by starting from our Hardy-like proof, one can establish the stronger noncontextuality inequality, for which the quantum-classical ratio is higher with the same $n$, which provides a new method to construct some optimal noncontextuality inequalities. Our results offer a way for optimizing and enriching exclusivity graphs, helping to explore more abundant quantum properties.

1. INTRODUCTION

Ideal measurements yield the same outcome when repeated, even when other compatible measurements have been performed in between. Some predictions of quantum theory for ideal measurements cannot be explained under the assumption that ideal measurements reveal preexisting outcomes that are independent of the context (i.e., the set of compatible measurements that have been jointly measured), this is known as quantum contextuality or Kochen–Specker (KS) contextuality [1]. Quantum contextuality is an intrinsic signature of nonclassicality as its classical simulation requires memory [2] and thermodynamical cost [3]. Moreover, it has been proven that quantum contextuality is necessary for fault-tolerant quantum computation via magic state distillation and measurement-based quantum computation [4]. Quantum contextuality also plays a fundamental role in some quantum key distribution protocols [5] and is crucial for understanding the underlying physics behind the limitation of quantum correlations [6]. So far, quantum contextuality has been experimentally observed in trapped ions [7], photons [8], ensembles of molecular nuclear spins in the solid state [9], and superconducting systems [10].

Copy Citation Text
Wen-Rong Qi, Jie Zhou, Ling-Jun Kong, Zhen-Peng Xu, Hui-Xian Meng, Rui Liu, Zhou-Xiang Wang, Chenghou Tu, Yongnan Li, Adán Cabello, Jing-Ling Chen, Hui-Tian Wang. Stronger Hardy-like proof of quantum contextuality[J]. Photonics Research, 2022, 10(7): 1582