Bias in Local Spin Measurements from Deformed Symmetries
arXiv:2603.08618
The paper investigates how local spin measurements on entangled singlet states are affected when rotational symmetry is modeled by a quantum group, showing that conventional and braided measurement prescriptions yield deformation-dependent biases.
Abstract
We study local spin measurements on bipartite singlet states when rotational symmetry is described by a quantum group rather than an ordinary Lie group. Although the fundamental spin-1/2 representation has the usual one-particle action on states, the non-trivial coproduct selects a deformed analogue of the Bell singlet state. We show that conventional tensor-factor measurements on this invariant singlet lead to deformation-dependent one-site outcome statistics. We then compare this standard-local prescription with a braided-local one, obtained by dressing local observables with the R-matrix and using the corresponding braided inner product. The braided observables are covariant under the Hopf adjoint action, but define a distinct measurement structure and lead to the reciprocal bias on the deformed singlet state.
14 pages, no figures. Extended and substantially revised version. Discussion and interpretation updated; main result unchanged