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Physicists describe nature using mathematics as the natural language, and forquantum mechanics, it prefers to use complex numbers. However, whether complexnumbers are really necessary for the theory has been debated ever since itsbirth. Recently, it has been shown that a three-party correlation created inentanglement swapping scenarios comprising independent states and measurementscannot be reproduced using only real numbers. Previous experiments haveconceptually supported the predication, yet not satisfying the independentstate preparations and measurements simultaneously. Here, we implement such atest with two truly independent sources delivering entangled photons to threeparties under strict locality conditions. By employing fast quantum randomnumber generators and high-speed polarization measurements, we space-likeseparate all relevant events to ensure independent state preparations andmeasurements, and close locality loopholes simultaneously. Our results violatethe real number bound of 7.66 by 5.30 standard deviations, hence rejecting theuniversal validity of the real-valued quantum mechanics to describe nature.

Experimental refutation of real-valued quantum mechanics under strict locality conditions