Source-linked AI summary
A simple test for hidden variables in spin-1 system
Alexander A. Klyachko, M. Ali Can, Sinem Binicioğlu, Alexander S. Shumovsky
TL;DR
The paper asks whether nonclassicality can be detected in a three-dimensional spin-1 state before decay, addressing the status of hidden-variable descriptions. It constructs a pentagram Bell-type inequality and finds that every spin-1 state except coherent states is nonclassical, while existing experimental data lack sufficient precision to verify the violation.
Problem
The paper asks whether one can detect nonclassicality in the neutrally polarized spin-1 state |0⟩ before decay, addressing hidden-variable descriptions in a three-dimensional system.
Method
The authors construct a pentagram Bell-type inequality using five cyclically orthogonal spin-projection operators and formulate hidden variables through compatible joint probability distributions.
Results
Every spin-1 state is nonclassical except coherent states, which pass the test for any pentagram; neutrally polarized states exhibit especially extreme nonclassical behavior.
Takeaways & Limitations
The pentagram inequality tests arbitrary hidden-variable models, including context-free and contextual models, while reducing the required spin projections from 31 to 5.
Takeaways & Limitations
Available raw experimental data fall below the theoretical curve near δ = 0.8383 and lack the precision required to demonstrate a violation of classical realism.
Abstract
from arXiv · showhide
We resolve an old problem about the existence of hidden parameters in a three-dimensional quantum system by constructing an appropriate Bell's type inequality. This reveals a nonclassical nature of most spin-$1$ states. We shortly discuss some physical implications and an underlying cause of this nonclassical behavior, as well as a perspective of its experimental verification.