English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

It is pointed out that the local hidden variables model of Bell andClauser-Horne-Shimony-Holt (CHSH) gives $||\leq 2\sqrt{2}$ or $||\leq 2$for the quantum CHSH operator $B={\bf a}\cdot {\bf \sigma}\otimes ({\bf b}+{\bfb}^{\prime})\cdot {\bf \sigma} +{\bf a}^{\prime}\cdot{\bf \sigma}\otimes ({\bfb}-{\bf b}^{\prime})\cdot{\bf \sigma} $ depending on two different ways ofevaluation, when it is applied to a $d=4$ system of two spin-1/2 particles.This is due to the failure of linearity, and it shows that the conventionalCHSH inequality $||\leq 2$ does not provide a reliable test of the $d=4$local non-contextual hidden variables model. To achieve $||\leq 2$ uniquely,one needs to impose a linearity requirement on the hidden variables model,which in turn adds a von Neumann-type stricture. It is then shown that thelocal model is converted to a factored product of two non-contextual $d=2$hidden variables models. This factored product implies pure separable quantumstates and satisfies $||\leq 2$, but no more a proper hidden variables modelin $d=4$. The conventional CHSH inequality $||\leq 2$ thus characterizes thepure separable quantum mechanical states but does not test the model of localhidden variables in $d=4$, to be consistent with Gleason's theorem whichexcludes non-contextual models in $d=4$. This observation is also consistentwith an application of the CHSH inequality to quantum cryptography by Ekert,which is based on mixed separable states without referring to hidden variables.

Does CHSH inequality test the model of local hidden variables?