A camera looks at two distant sparks. They're so close together that they merge into a single fuzzy blob. It seems impossible to tell them apart — the classic limit of optical microscopy has been reached.

But quantum mechanics hints that the light field still holds a secret about where each spark sits. The information hasn't vanished: it's just hidden in the structure of the blob itself. The authors tackled the three-dimensional case and mathematically squeezed out the quantum precision limit for estimating the full distance between two incoherent sources. It turns out that even when one spark dims against the other, the precision doesn't drop to zero. It holds thanks to a second-order tensor — a quantity that describes how the blob shifts with tiny displacements. This tensor, like a built-in compass, points to the best direction for measurement. If the point spread function (the blob's shape) has mirror symmetries, you can find the optimal orientation of the two sources almost by eye, just by looking at the symmetry axes.

For the most common three-dimensional Gaussian blur, the response tensor turned out to be directly proportional to the inverse matrix of the blob's spatial uncertainty. In simpler terms, the more elongated the blob is in a given direction, the more precisely you can measure distances along that axis. The geometry of the blur and quantum precision are directly linked, with no extra assumptions.

So abstract geometry turns into practical advice: without changing the optics, just by physically rotating the system, you can squeeze out maximum resolution. The idea is as simple as turning a pair of binoculars, but it's backed by rigorous quantum calculations. And then two sparks that seemed indistinguishable regain their depth — the camera sees a three-dimensional distance where there was only a flat blob before.