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.