### 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.

Original language | English |
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Article number | 15 |

Journal | Communications Physics |

Volume | 2 |

Issue number | 1 |

DOIs | |

Publication status | Published - Dec 1 2019 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Communications Physics*,

*2*(1), [15]. https://doi.org/10.1038/s42005-019-0114-z

**Disproving hidden variable models with spin magnitude conservation.** / Kurzyński, Paweł; Laskowski, Wiesław; Kołodziejski, Adrian; Pál, K.; Ryu, Junghee; Vértesi, T.

Research output: Contribution to journal › Article

*Communications Physics*, vol. 2, no. 1, 15. https://doi.org/10.1038/s42005-019-0114-z

}

TY - JOUR

T1 - Disproving hidden variable models with spin magnitude conservation

AU - Kurzyński, Paweł

AU - Laskowski, Wiesław

AU - Kołodziejski, Adrian

AU - Pál, K.

AU - Ryu, Junghee

AU - Vértesi, T.

PY - 2019/12/1

Y1 - 2019/12/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85071162672&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85071162672&partnerID=8YFLogxK

U2 - 10.1038/s42005-019-0114-z

DO - 10.1038/s42005-019-0114-z

M3 - Article

AN - SCOPUS:85071162672

VL - 2

JO - Communications Physics

JF - Communications Physics

SN - 2399-3650

IS - 1

M1 - 15

ER -