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arXiv · 2103.08123

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·Ming Gong·Hui Deng·Futian Liang·Qiang Zhang·Cheng-Zhi Peng·Xiaobo Zhu·Adan Cabello·Chao-Yang Lu·Jian-Wei Pan
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Abstract

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 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 in the maximum game scores between a high-fidelity multi-qubit quantum experiment and players using only real-number quantum theory. Here, using superconducting qubits, we faithfully experimentally implement the quantum game based on entanglement swapping with a state-of-the-art fidelity of 0.952(1), which beats 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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Ming-Cheng Chen, Can Wang, Feng-Ming Liu, Jian-Wen Wang, Chong Ying, Zhong-Xia Shang, Yulin Wu, Ming Gong, Hui Deng, Futian Liang, Qiang Zhang, Cheng-Zhi Peng, Xiaobo Zhu, Adan Cabello, Chao-Yang Lu, Jian-Wei Pan. 2022-02-12. Ruling out real-valued standard formalism of quantum theory. https://doi.org/10.1103/physrevlett.128.040403

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