Ruling Out Real-Valued Standard Formalism of Quantum Theory

被引：64

作者：

Chen, Ming-Cheng ^{[1
,2
,3
,4
]}

Wang, Can ^{[1
,2
,3
,4
]}

Liu, Feng-Ming ^{[1
,2
,3
,4
]}

Wang, Jian-Wen ^{[1
,2
,3
,4
]}

Ying, Chong ^{[1
,2
,3
,4
]}

Shang, Zhong-Xia ^{[1
,2
,3
,4
]}

Wu, Yulin ^{[1
,2
,3
,4
]}

Gong, M. ^{[1
,2
,3
,4
]}

Deng, H. ^{[1
,2
,3
,4
]}

Liang, F-T ^{[1
,2
,3
,4
]}

Zhang, Qiang ^{[1
,2
,3
,4
]}

Peng, Cheng-Zhi ^{[1
,2
,3
,4
]}

Zhu, Xiaobo ^{[1
,2
,3
,4
]}

Cabello, Adan ^{[5
,6
]}

Lu, Chao-Yang ^{[1
,2
,3
,4
]}

Pan, Jian-Wei ^{[1
,2
,3
,4
]}

机构：

[1] Univ Sci & Technol China, Hefei Natl Lab Phys Sci Microscale, Hefei 230026, Anhui, Peoples R China

[2] Univ Sci & Technol China, Dept Modern Phys, Hefei 230026, Anhui, Peoples R China

[3] Univ Sci & Technol China, CAS Ctr Excellence & Synerget Innovat Ctr Quantum, Shanghai 201315, Peoples R China

[4] Shanghai Res Ctr Quantum Sci, Shanghai 201315, Peoples R China

[5] Univ Seville, Dept Fis Aplicada 2, E-41012 Seville, Spain

[6] Univ Seville, Inst Carlos I Fis Teor & Computac, E-41012 Seville, Spain

来源：

PHYSICAL REVIEW LETTERS | 2022年 / 128卷 / 04期

基金：

国家重点研发计划; 中国国家自然科学基金;

关键词：

36;

D O I：

10.1103/PhysRevLett.128.040403

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

Standard quantum theory was formulated with complex-valued Schrodinger equations, wave functions, operators, and Hilbert spaces. Previous work attempted to simulate quantum systems using only real numbers by exploiting an enlarged Hilbert space. A fundamental question arises: are the complex numbers really necessary in the standard formalism of quantum theory? To answer this question, a quantum game has been developed to distinguish standard quantum theory from its real-number analog, by revealing a contradiction between a high-fidelity multiqubit quantum experiment and players using only real-number quantum theory. Here, using superconducting qubits, we faithfully realize the quantum game based on deterministic entanglement swapping with a state-of-the-art fidelity of 0.952. Our experimental results violate the real-number bound of 7.66 by 43 standard deviations. Our results disprove the real-number formulation and establish the indispensable role of complex numbers in the standard quantum theory.

引用

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