期刊
PHYSICAL REVIEW LETTERS
卷 128, 期 4, 页码 -出版社
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevLett.128.040403
关键词
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资金
- National Natural Science Foundation of China [91836303, 11805197]
- National Key R&D Program of China
- Chinese Academy of Sciences
- Anhui Initiative in Quantum Information Technologies
- Science and Technology Commission of Shanghai Municipality [2019SHZDZX01]
- MCIN/AEI [PID2020-113738GB-I00]
- Project Qdisc (Universidad de Sevilla) [US-15097]
- FEDER funds
- QuantERA grant SECRET (MCIN/AEI) [PCI2019-111885-2]
This study demonstrates the indispensable role of complex numbers in standard quantum theory through a quantum game, revealing the inconsistency of previous attempts to simulate quantum systems using only real numbers.
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.
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