Testing 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 first used to formulate quantum theory. Nonetheless, Erwin Schrödinger (one of its founding fathers) said in response to a letter from Hendrik Lorenz: "The use of complex numbers in quantum theory is inconvenient and should be avoided. The wave function is unquestionably a real function at its core."

Bell tests have recently been used to convincingly rule out any local hidden variable explanation of quantum theory. Such tests were then expanded to include a network with numerous independent hidden variables. Quantum theory with only real numbers, or "real quantum theory," and standard quantum theory yield quantitatively different predictions in specific scenarios in such a quantum network, allowing experimental tests of real quantum theory's validity.

One of these tests was recently altered by researchers from China's Southern University of Science and Technology, the Austrian Academy of Sciences, and other institutions around the world so that it may be used in cutting-edge photonic systems. Their article, which was published in Physical Review Letters, shows that quantum correlations exist in an optical network that are not described by genuine quantum theory.

"Complex numbers have been considered more as a mathematical connivence than a fundamental building component since the early days of quantum theory," Zizhu Wang, one of the study's authors, told. "The argument over the role of complex numbers in quantum theory has raged on till now."

Ernst Stueckelberg, a Swiss physicist, and his colleagues successfully defined quantum theory in real Hilbert spaces in the 1960s. While this was a significant step forward in the industry, their formulation did not use the well-known "tensor product" to combine several systems. This basically indicates that their formulation contradicts what is known as "true quantum theory."

"When we started looking at quantum theory from an information-theoretic perspective, interest in this subject was reignited," Wang explained. "In some information processing tasks, generalised probabilistic theories (GPTs) formulated with only real numbers turn out to be as powerful as quantum theory, and even outperform quantum theory in others. We didn't have the tools to definitely rule out real quantum theory as a viable alternative to complex quantum theory until today, despite the fact that GPTs have correlations beyond quantum theory."

Fan and his colleagues' current paper is inspired by a long-standing controversy in the physics community, especially the presence of local hidden variables in quantum theory. In one of their seminal publications, published in 1935, physicists Albert Einstein, Boris Podolsky, and Nathan Rosen presented this critical subject. While many physicists later investigated this subject, no one was able to come up with a specific mechanism to evaluate whether these local hidden variables exist for decades.

"In 1964, John Bell came up with the innovative idea of inferring fundamental features of physical systems using correlations functions of probabilities, which can be evaluated and examined in a laboratory," Jingyun Fan, another researcher involved in the study, told Phys.org. "It took another 50 years to finally settle this argument and rule out local hidden variable explanations of quantum theory in a systematic manner."

While Bell's theorem has been used effectively in numerous investigations, it is insufficient to precisely forecast the differences between real and complex quantum theories. Fan and his colleagues were able to evaluate these disparities in their current study by evaluating a quantum network with several, independent sources.

"Recently, a group of theorists from Vienna, Barcelona, and Geneva, led by Miguel Navascués, Mirjam Weilenmann, Armin Tavakoli, David Trillo, and Thinh P. Le, discovered that a natural generalisation of the Bell test in a network can distinguish complex quantum theory from real quantum theory," Fan said. "Real quantum theory does not agree with the predictions of complex quantum theory in a network in which participants are connected through numerous independent entanglement sources. This paves the path for a quantum network based on independent entanglement sources to be used to experimentally discriminate between the two theories."

The researchers employed a state-of-the-art optical quantum network to develop and evaluate the theory devised by Navascués and his colleagues in an experimental scenario. Source independence is a major premise of the theory, which indicates that the investigated network should be made up of independent entanglement sources that produce pairs of entangled states.

Predictions become invalid, according to the theory, if this assumption is not met. Fan and his colleagues employed a photonic network in which sources of entangled photons are physically separated to ensure that it was met in their experiments.

"Another experimental obstacle is that the experimental system must be noise-free," Fan explained. "These challenges were overcome by a team of scientists from Southern University of Science and Technology in Shenzhen, including Zhengda Li, Yali Mao, Hu Chen, Lixin Feng, Shengjun Yang, and myself, as well as Zizhu Wang from the University of Electronic Science and Technology of China in Chengdu, the city famous for its pandas," Fan said. "We built a quantum network experiment with two independent entanglement sources and three parties (Alice, Bob, and Charlie) and discovered correlations that violated real quantum theory requirements by more than 4.5 standard deviations."

Standard tests based on Bell's theory, in contrast to Fan and his colleagues' experimental test, only use a single entanglement source and consider two parties (i.e., Alice and Bob). The researchers were able to overcome the difficulties associated with typical Bell's theorem-based testing and efficiently assess the differences between real and complex quantum theories thanks to their experimental setup.

"Our experiment demonstrates that not all predictions based on normal quantum theory with complex numbers can be described by the real-number counterpart of conventional quantum theory," Fan said. "Complex numbers, as a result, are important to quantum theory."

The latest study conducted by this group of academics could pave the door for more research into the foundations of quantum physics, particularly in quantum networks, in the future. Because Bell's theorem is frequently employed in quantum information science, this could eventually lead to the development of new revolutionary quantum technologies and applications.

"While Bell nonlocality in a bipartite system is already perplexing, multipartite nonlocality in our many-body universe is even more so: nature's correlations are boundlessly multipartite nonlocal," Fan continued. "Interestingly, we just did the first experiment and established a Bell-type test for genuine multipartite nonlocality in networks to show that nature is unbounded multipartite nonlocal."

References:

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