Quantum distance refers to a measure of quantum mechanical similarity between two quantum states. A quantum distance of one means that the two quantum states are the same, whereas a quantum distance of zero implies that they are exactly the opposite. Physicists introduced this concept in the realm of theoretical science a long time ago, but its importance has been increasingly recognized in the field of physics only in recent times.
In the last few years, many experimental physicists have tried to measure the quantum distance of electrons in real solid-state materials, but a direct measurement of the quantum distance and thus quantum metric tensor—a key geometric quantity in modern physics defined in terms of the distance between nearby quantum states—has remained elusive so far. Since the quantum metric tensor is highly relevant in explaining and understanding fundamental physical phenomena in solids, it is, therefore, crucial to come up with an effective methodology for its direct measurement in solid-state systems.
In a recent breakthrough in theoretical as well as experimental quantum physics, an international team of researchers from the Republic of Korea and the USA, led by Keun Su Kim, an Underwood Distinguished Professor of Physics and Director of the Center for Bandstructure Engineering at the Department of Physics at Yonsei University, Republic of Korea, have reported the first experimental measurement of the quantum distance. Their findings were made available online and published in the journal Science on 5 June 2025.
The research was carried out in close collaboration between an experimental group led by Prof. Kim with Yoonah Chung and Soobin Park at Yonsei University and a theory group led by Professor Bohm-Jung Yang with Sunje Kim and Yuting Qian at Seoul National University.
According to Prof. Kim, "The theory group found that one of the elemental layered crystals, black phosphorus, is an ideal material to study the quantum distance of electrons owing to its structural simplicity. Based on this input, the experimental group measured the quantum distance of electrons in black phosphorus using the momentum space distribution of the pseudospin texture of the valence band from the polarization dependence of angle-resolved photoemission spectroscopy technique and synchrotron radiation via Advanced Light Source in the USA."
In this way, the researchers successfully measured the full quantum metric tensors of Bloch electrons in solids in black phosphorus for the first time.
"Measuring the quantum distance is fundamentally important not only to understand anomalous quantum phenomena in solids, including special ones such as superconductors, but also to advance our quantum science and technologies. As an example, a precise measure of quantum distances would help develop fault-tolerant quantum computation technologies," explains Prof. Kim.
As it is of fundamental importance to understand materials at the quantum mechanical level, the quantum distance is one of the cornerstones with which we can fully understand complex quantum phenomena of solids. This type of research will lead us to better semiconductor technologies, higher and higher transition-temperature superconductors, and superior quantum computers over conventional computers.
Overall, this work is expected to provide insights into quantum geometric responses in a wide class of crystalline systems and eventually pave the way for a quantum technology-led future.
