Sometimes there are properties in quantum systems that are measurable not because of the state itself, but because of the history of the system, for e.g. the to

Sometimes there are properties in quantum systems that are measurable not because of the state itself, but because of the history of the system, for e.g. the topology that an electron travels through. A good example of this is the quantum Hall effect, where you get discrete jumps in the conductance across 2D systems in which a voltage is applied in a transverse direction. This is caused by Berry Curvature, which is the real part of a geometric tensor that describes the topology of the quantum state. The imaginary part of the same tensor is called the “quantum metric”. In this specific case, they’re measuring a different voltage due to electrons passing through the data written in the antiferromagnet. They pose theoretically in the paper that it could be because of an effect of the quantum metric