The local Bloch radius as an entanglement readout: what the qg symmetry filter restores and what it does not

Each qubit’s local qg values are a point in the Bloch ball. Its squared distance from the centre, , is the radius of the sphere on which the qubit lives (area ). For a pure register the deficit is the known one-tangle of the qubit with the rest; with noise it mixes entanglement and impurity. We show that circuits which conserve the Hamming weight remove this ambiguity under one noise model. In a state of fixed weight on every qubit, so and the deficit is read from Z-basis shots alone; under equal amplitude damping the qg symmetry filter returns the noiseless state exactly, so the filtered deficit is the noiseless one-tangle. In a pre-registered simulation (90 configurations) the filtered deficit equals it to , and on product states it is exactly zero, while the unfiltered readout reports a false deficit of 0.60–0.95. On five device noise models (three IBM backends, two IonQ) the filter cuts the deficit error of trained circuits 3.2–4.0 times, but it removes only 15–33% of the false deficit of a product state: errors that move an excitation inside the sector survive the filter, and near a pole the deficit amplifies them as . The radius also separates the polar angle in radians from the length of the vector, : this angle is exact under depolarizing noise, where $\arccosqg_Z$ errs by up to 0.7 rad, and it is 5–9 times more accurate on the device noise models once the noise gates are actually executed. Three of nineteen predictions failed and are reported. Everything is reproduced by the open-source library qang (version 0.6.8, pip install qang).