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Ruling Out Real-Valued Standard Formalism of Quantum Theory

Ming-Cheng Chen, Can Wang, Feng-Ming Liu, Jian-Wen Wang, Chong Ying, Zhong-Xia Shang, Yulin Wu, M. Gong, H. Deng, F.-T. Liang, Qiang Zhang, Cheng-Zhi Peng, Xiaobo Zhu, Adán Cabello, Chao-Yang Lu, and Jian-Wei Pan
Phys. Rev. Lett. 128, 040403 – Published 24 January 2022
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Abstract

Standard quantum theory was formulated with complex-valued Schrödinger 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.

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  • Received 30 November 2021
  • Accepted 7 December 2021

DOI:https://doi.org/10.1103/PhysRevLett.128.040403

© 2022 American Physical Society

Physics Subject Headings (PhySH)

Quantum Information, Science & TechnologyGeneral Physics

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Quantum Mechanics Must Be Complex

Published 24 January 2022

Two independent studies demonstrate that a formulation of quantum mechanics involving complex rather than real numbers is necessary to reproduce experimental results.

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Authors & Affiliations

Ming-Cheng Chen1,2,3,*, Can Wang1,2,3,*, Feng-Ming Liu1,2,3,*, Jian-Wen Wang1,2,3, Chong Ying1,2,3, Zhong-Xia Shang1,2,3, Yulin Wu1,2,3, M. Gong1,2,3, H. Deng1,2,3, F.-T. Liang1,2,3, Qiang Zhang1,2,3, Cheng-Zhi Peng1,2,3, Xiaobo Zhu1,2,3, Adán Cabello4,5, Chao-Yang Lu1,2,3, and Jian-Wei Pan1,2,3

  • 1Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
  • 2CAS Centre for Excellence and Synergetic Innovation Centre in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
  • 3Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
  • 4Departamento de Física Aplicada II, Universidad de Sevilla, E-41012 Sevilla, Spain
  • 5Instituto Carlos I de Física Teórica y Computacional, Universidad de Sevilla, E-41012 Sevilla, Spain

  • *These authors contributed equally to this work.

See Also

Testing Real Quantum Theory in an Optical Quantum Network

Zheng-Da Li, Ya-Li Mao, Mirjam Weilenmann, Armin Tavakoli, Hu Chen, Lixin Feng, Sheng-Jun Yang, Marc-Olivier Renou, David Trillo, Thinh P. Le, Nicolas Gisin, Antonio Acín, Miguel Navascués, Zizhu Wang (王子竹), and Jingyun Fan
Phys. Rev. Lett. 128, 040402 (2022)

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Vol. 128, Iss. 4 — 28 January 2022

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