Hidden in thin semiconductor films are anyons — traveling particles that remember their path. Their memory was predicted by Frank Wilczek, and Alexei Kitaev showed how to use it to build a quantum computer that is immune to errors. But first, one needs to measure the anyon's entropy — a measure of its hidden complexity, or memory capacity. The higher it is, the more information the particle can hold. Physicists proposed weighing the anyon on ultra-sensitive electrical 'scales' — an interferometer. When a particle jumps into a trap inside the device, the current starts to tremble, changing intensity in jumps. This is like scales that oscillate more strongly the more facets the diamond being weighed has. By analyzing the statistics of these jumps, scientists recover the charge (just one quarter of an electron’s charge!) and the number of hidden states. This is how quantum sensing works — a delicate measurement without destruction. Strikingly, for the most promising type of anyons, the entropy equals exactly √2 ≈ 1.414 — a mathematical constant from geometry, rarely seen in particle physics. Computer simulations (numerical modeling) confirm: for the '5/2' state, the entropy of a single anyon is about 0.35 of Boltzmann's constant — almost half that of an electron. The entire process is immune to quantum decoherence, so quantum measurements become a practical verification tool. Experimental confirmation of these numbers will be long-awaited proof of the existence of anyons with memory and will pave the way to topological computers.