Quantum mechanics must be plural! CSU completes verification under strict fixed domain conditions for the first time

In early 2022, Pan Jianwei's and Lu Chaoyang's teams at the University of Science and Technology of China and Fan Jingyun's team at the Southern University of Science and Technology independently experimentally excluded the standard quantum mechanics in real form. Among them, Fan's team used a "partial" Bell state measurement in their experiment, while Pan's team performed a complete Bell state measurement.

But the story does not end there. Just like the history of the Bell inequality test that won the Nobel Prize in Physics this year, from John Clauser's experiment in 1972, to Alain Aspect's experiment in 1982, to Anton Zeilinger's experiment in 1996, and the three teams that completed a loophole-free Bell inequality experiment in 2015. Experimental scientists have been working continuously to close various potential loopholes to obtain more precise experimental proofs.

In the independent work of the two teams earlier in the year, there were problems with fixed (or local) domains, measurement independence, and entangled source independence because the requirements of space-like separation could not be met at distance.

In order to test the objective existence of complex numbers more rigorously, Pan Jianwei, Lu Chaoyang, and Zhang Qiang from the University of Science and Technology of China, in collaboration with researchers from the Jinan Institute of Quantum Technology and other institutions, have examined quantum mechanics in the form of real numbers using entangled exchange optical quantum networks with space-like partitions, closing the loopholes of fixed-domain, measurement independence, and entangled source independence for the first time in the international arena [1].

The related research results have been published in the prestigious international academic journal Physical Review Letters [2] and written about in the APS News section of the American Physical Society [3].

01Why do quantum physicists insist on using real numbers?

Complex numbers include real and imaginary numbers. Complex numbers are widely utilized in classical and relativistic physics. For example, in electromagnetism it greatly simplifies the description of wave-like phenomena. However, in these physical theories, complex numbers are not necessary because all meaningful sizable measurements can be represented by real numbers. Thus, complex number analysis is just a powerful computational tool.

But it has been a long-standing fundamental question as to whether quantum physics does require the involvement of complex numbers.

In 1926, the physicist Schrödinger, when establishing the fluctuation equations, initially wrote down the differential equation for mechanical particles with reference to the model of fluctuating optics, but this equation did not make any physical sense, however, when he put the square root i of negative 1 into the equation, the wave function in complex form instantly became meaningful and could help us to accurately describe the quantum behavior of particles [4].

However, the square of the modulus of the wave function describes the probability of the appearance of the particle, and although the wave function is written in the complex form, the probability itself is still a real number. So, is the imaginary number i really necessary to describe the real world? Schrödinger was not sure.

In his letter to Lorentz, Schrödinger stated that the wave function was not very down-to-earth itself by introducing complex numbers, and that essentially the quantum wave function should be a real function. Schrödinger had been trying to erase the complex numbers from his wave equations, but had not succeeded.

Schrödinger's equation

From the early days of quantum mechanics, physicists have argued that many features of quantum theory in the framework of complex numbers are represented by two alternative hypothetical theories, such as the Hilbert space of complex numbers can be replaced by a Hilbert space of real or quaternion numbers.

Many attempts at real number quantum mechanics have been made from Schrödinger to von Neumann, Ernst Stickelberg, Freeman Dyson, Nicolas Gisin, and William Wootters. These studies led physicists to believe for a while that complex numbers were only there for our convenience in quantum mechanics as a means of computation and not as a necessity, as if we could describe our world entirely in terms of real numbers only.

02The nail in the coffin! Quantum mechanics must be complex

In January 2021, a team of researchers from Austria, Spain and Switzerland proposed a method to test the type of Bell inequality that verifies the necessity of complex numbers using deterministic entanglement exchange [5]. The unique feature of this scheme is that it is experimentally testable, quantitative, and similar to the Bell inequality criterion.

As shown in the figure below, Alice, Bob, and Charlie perform a three-way experiment similar to Bell's inequality. Two sources distribute entangled quantum bits between Alice and Bob and Bob and Charlie, respectively. Each party independently chooses from a set of possibilities the measurements to be made on its quantum bits. Since the sources are independent, the quantum bits sent to Alice and Charlie are initially uncorrelated, and Bob receives a quantum bit from both sources and, by performing a Bell state measurement, he generates entanglement between Alice's and Charlie's quantum bits, even though these quantum bits never interact - a process called "entanglement. -This process is called "entanglement swapping".

Image from APS Physics

In simple terms, two sources distribute the entangled quantum bits to three observers, who calculate the "score" from the measurement of the quantum bits. In this theoretical framework, the real number form of the bound is 7.66, while experimental tests earlier in the year showed 8.09, exceeding the criterion by 43 standard deviations. The experimental findings support the need for quantum physics to use complex numbers [6].

Plot of experimental results: Different theories correspond to different numerical bounds, and the experimental measurements by Pan's team greatly exceed the real quantum mechanical model. Image from Mingcheng Chen, Chon Wang, Fengming Liu, et al. PRL 128, 040403 (2022)

His gate uses an I-shaped transmon quantum bit design to increase the spacing between quantum bits. Through a high-precision quantum manipulation technique, two sequences of entangled pulses are used to prepare two pairs of entangled states, distributing the quantum bits to the three parties involved. Each party independently selects the measurement operation to be performed on its quantum bits, where Bob performs a complete Bell state measurement.

However, the work utilizes four quantum bits on the same superconducting quantum chip at a distance that does not satisfy the spacelike separation requirement, and thus suffers from problems of fixation, measurement independence, and entanglement source independence.

Therefore, in order to more rigorously test the objective existence of complex numbers, Pan's team used two independent sources in the network to independently generate entangled photon pairs, which were distributed to three participants at a distance for high-speed random photon measurement operations, based on the spacelike spacedependent entangled exchange optical quantum network, as shown in the figure below. During the experiment, the participants are not affected by the measurement choices and results of other participants, and each independently performs the local random operation.

Schematic diagram of the experiment. The portraits show the three tied first authors, from left to right, Xuemei Gu, Dian Wu, and Yangfan Jiang.

The experiments are spread over five locations, each at least 89 meters apart, ensuring that information needs to propagate from one part of the experiment to another at speeds greater than the speed of light to interfere with the results. This precaution was intended to help rule out the possibility of unknown mechanisms (at least those allowed by the current laws of physics) affecting the experiments.

The experimental results exceed the quantum mechanical predictions of the real form by 5.3 standard deviations, rigorously verifying the indispensability of complex numbers in quantum mechanics. For the first time internationally, the loopholes of definiteness, measurement independence, and entangled source independence were closed.

In an interview with APS, William Wooters, professor emeritus of physics at Williams College, said, "The purpose of this kind of experiment is to rule out a class of theories, and if there are still these loopholes, you haven't really done that. So, it's good to close the loopholes."

Marc-Olivier Renou, a researcher at the Spanish Institute of Photon Science who is one of the authors of the 2021 theory proposal, says that the important loophole in independent sources can never be completely closed, but in the future, researchers may be able to quantify how much of this loophole is closed.

In this new paper, the researchers admit that it is "impossible to rule out all vulnerabilities" without making assumptions. The new experiment has a detection loophole, a loophole that was closed in previous experiments. Professor Lu Chaoyang said the KU team hopes to develop new techniques to enable an experiment that also closes vulnerabilities.

Reference links：

[1]http://news.ustc.edu.cn/info/1055/80843.htm

[2]https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.129.140401

[3]https://www.aps.org/publications/apsnews/202211/numbers.cfm

[4]https://mp.weixin.qq.com/s/nmgZIDa8okd9ze0kF0baGQ

[5]https://www.nature.com/articles/s41586-021-04160-4

[6]http://news.ustc.edu.cn/info/1055/78317.htm