Bias in Local Spin Measurements from Deformed Symmetries

TL;DR

This paper investigates how quantum group symmetries deform local spin measurement outcomes, revealing that traditional tensor-factor observables lead to biased statistics, which can be corrected by a symmetry-covariant approach.

Contribution

It introduces a framework for understanding local measurements under quantum group symmetries, highlighting the need for a braided locality concept to ensure unbiased results.

Findings

Conventional local observables produce deformation-dependent bias.

Symmetry-covariant R-matrix-dressed observables restore unbiased statistics.

Quantum group symmetries deform the notion of locality and measurement outcomes.

Abstract

We study bipartite spin-singlet correlations when rotational symmetry is described by a quantum group rather than an ordinary Lie group. We show that, even though the single-spin observables act as in the undeformed theory, the non-trivial coproduct reshapes the notion of "total" symmetry and leads to a deformed analogue of the Bell singlet state. We show that implementing local measurements with the conventional tensor-factor observables yields a striking effect: perfect anticorrelation is preserved, yet the one-site outcome statistics become deformation-dependent and biased. Using instead the symmetry-covariant, R-matrix-dressed embedding of local observables restores unbiased statistics while maintaining perfect anticorrelation. Our results demonstrate that, in a quantum group symmetry setting, strict tensor-factor locality is not stable under the symmetry and must be replaced by a braided notion of locality to formulate consistent local measurements.