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Physicists test real quantum theory in an optical quantum network
Zheng-Da Li and Ya-Li Mao preparing the experiment. Credit: Li et al.

Complex numbers were used to formulate quantum theory. When responding to a letter by Hendrik Lorenz, one of its founding fathers wrote, "using complex numbers in quantum theory is unpleasant and should be objected to." The wave function is a real function.

Scientists used Bell tests to rule out a hidden explanation of quantum theory. The tests were generalized to the network with multiple hidden variables. In a quantum network, quantum theory with only real numbers, or real quantum theory, and standard quantum theory make quantitatively different predictions in some scenarios, enabling experimental tests of the validity of real quantum theory.

The Austrian Academy of Sciences, the Southern University of Science and Technology in China, and other institutions worldwide have recently adapted one of these tests so that they could be used in state-of-the-art optical systems. The existence of quantum correlations in an optical network can't be explained by quantum theory.

From the beginning of quantum theory, complex numbers were treated more as a mathematical connivence than a fundamental building block, according to one of the researchers who carried out the study.

The Swiss physicist and his colleagues formulated quantum theory in real spaces. This was an important milestone in the field, but their formula didn't use the renowned, so-called "tensor product" to compose different systems. This basically means that their formula is not in line with real quantum theory.

When we started looking at quantum theory from an information-theoretic perspective, interest in this question was revived. Even though we know GPTs contain correlations beyond quantum theory, we did not have the tools to rule out real quantum theory as a viable alternative to complex quantum theory.

The recent paper by Fan and his colleagues draws inspiration from a long-standing debate in the physics field regarding the existence of local hidden variables in quantum theory. In 1935, Albert Einstein, Boris Podolsky and Nathan Rosen wrote a paper about this important question. For decades, no one was able to come up with a method to test whether these hidden variables exist.

In 1964, John Bell came up with the idea of using correlations functions of probabilities, which can be tested and analyzed in a laboratory, to infer underlying properties of physical systems.

Bell's theorem can be applied in many studies, but it is not enough to accurately predict the differences between real and complex quantum theories. Fan and his colleagues were able to assess the differences by looking at a quantum network.

A group of theorists, including David Trillo and Thinh P. Le from Vienna, have recently been formed. The way for distinguishing between the two theories in a quantum network based on independent sources is now possible.

The researchers used a state-of-the-art optical quantum network to implement and test the theory. A key assumption of the theory is source independence, which means that the analyzed network should consist of independent sources.

Predictings become invalid when the assumption is not met. To ensure that it was met in their experiments, Fan and his colleagues used a network in which sources of entangled photons are physically separated.

The experimental system must be clean with very little noise, according to Fan.

Standard tests based on Bell's theory only use a single source and consider two parties, unlike the experimental test carried out by Fan and his colleagues. The researchers were able to test the differences between real and complex quantum theories using their experimental setting.

The experiment shows that not all predictions based on standard quantum theory with complex numbers can be modeled by the real-number analog of standard quantum theory.

The recent study carried out by this team of researchers could lead to further research on the foundations of quantum physics. Bell's theorem is widely used in quantum information science and this could enable the development of new innovative quantum technologies and applications.

While the Bell nonlocality of a bipartite system is already counter-intuitive, multipartite nonlocality in our many-body world is even more so.

More information: Zheng-Da Li et al, Testing Real Quantum Theory in an Optical Quantum Network, Physical Review Letters (2022). DOI: 10.1103/PhysRevLett.128.040402

The test of genuine multipartite nonlocality was conducted by Ya-Li Mao, Zheng- Da Li, Sixia Yu, and Jingyun Fan.

Journal information: Physical Review Letters

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