In 1946, Felix Bloch predicted that even without an external magnetic field, a fluctuating magnetic moment exists in an ensemble of spins. It grows as the square root of the number of particles, and in small samples this noise can exceed thermal polarization. For a long time, it was described through phenomenological fluctuating fields, which required additional assumptions. The new work shows that the noise is a trace left by the measurements themselves, and it can be derived from the standard formalism of open quantum systems.

Imagine an interpreter who gets distracted by every rustle in the hall, turning a one-hour meeting into two. Similarly, a quantum system: each measurement leaves an imprint, changing its state. The authors built a model where the evolution of a spin ensemble is a sequence of quantum operations: measurement and evolution. The interaction with the environment is described by a CPTP map, and the interaction with the detector is described through measurement operators. For strong measurements, they use projectors onto subspaces with fixed magnetization; for weak measurements, they use POVM elements with a Gaussian profile.

The statistics of a second measurement correlate with the first, but the correlation vanishes for large time intervals or weak measurements. For arbitrary initial states, except for the first measurement, the statistics match the case of a mixed state. This means that the noise does not depend on how the system was prepared, provided enough time has passed.

Previously, spin noise was described via phenomenological fluctuating fields, which required additional assumptions. Now it is shown that the noise is fully determined by quantum measurements and evolution, without introducing random fields. This approach simplifies the analysis and opens the way to a unified description of noise in various quantum technologies.

The interpreter who was distracted by rustles eventually learned to ignore them. Likewise, scientists now see that noise is not an annoying nuisance but a direct consequence of how we pose questions to a quantum system. And the more precise the question, the louder the answer.