Disproving hidden variable models with spin magnitude conservation

TL;DR

This paper introduces a new test for local hidden variable models involving spin magnitude conservation, showing that quantum correlations violate these models more broadly than traditional Bell inequalities.

Contribution

It proposes a novel inequality based on spin magnitude conservation to disprove local hidden variable theories in quantum mechanics.

Findings

Quantum correlations violate the new inequalities more broadly than Bell inequalities.

Hidden variable models cannot simultaneously assign physical reality to spin vectors and predict measurement outcomes.

The results challenge the classical notion of fixed-length spin vectors in hidden variable theories.

Abstract

The squares of the three components of the spin-s operators sum up to $s(s+1)$. However, a similar relation is rarely satisfied by the set of possible spin projections onto mutually orthogonal directions. This has fundamental consequences if one tries to construct a hidden variable (HV) theory describing measurements of spin projections. We propose a test of local HV-models in which spin magnitudes are conserved. These additional constraints imply that the corresponding inequalities are violated within quantum theory by larger classes of correlations than in the case of standard Bell inequalities. We conclude that in any HV-theory pertaining to measurements on a spin one can find situations in which either HV-assignments do not represent a physical reality of a spin vector, but rather provide a deterministic algorithm for prediction of the measurement outcomes, or HV-assignments represent a physical reality, but the spin cannot be considered as a vector of fixed length.