Chen Ming-Cheng, Wang Can, Liu Feng-Ming, Wang Jian-Wen, Ying Chong, Shang Zhong-Xia, Wu Yulin, Gong M, Deng H, Liang F-T, Zhang Qiang, Peng Cheng-Zhi, Zhu Xiaobo, Cabello Adán, Lu Chao-Yang, Pan Jian-Wei
Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China.
CAS Centre for Excellence and Synergetic Innovation Centre in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China.
Phys Rev Lett. 2022 Jan 28;128(4):040403. doi: 10.1103/PhysRevLett.128.040403.
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.
标准量子理论是用复值薛定谔方程、波函数、算符和希尔伯特空间来表述的。先前的工作试图通过利用扩展的希尔伯特空间仅使用实数来模拟量子系统。一个基本问题出现了：复数在量子理论的标准形式中真的是必要的吗？为了回答这个问题，已经开发了一种量子博弈，通过揭示高保真多量子比特量子实验与仅使用实数量子理论的参与者之间的矛盾，来区分标准量子理论与其实数类似物。在此，我们使用超导量子比特，基于确定性纠缠交换，以0.952的最新保真度忠实地实现了该量子博弈。我们的实验结果比7.66的实数界限高出43个标准差。我们的结果反驳了实数表述，并确立了复数在标准量子理论中不可或缺的作用。
