A feasible experiment is discussed which allows us to prove a Bell's theorem for two particles without using an inequality. The experiment could be used to test local realism against quantum mechanics without the introduction of additional assumptions related to hidden variables states. Only assumptions based on direct experimental observation are needed.

Jan 1, 19960 citations

A Loophole-Free Test of Local Realism

Lynden K. Shalm

Bulletin of the American Physical SocietyOct 22, 20160 citations

STEAM-H: Science, Technology, Engineering, Agriculture, Mathematics & Health

Local Realism Without Hidden Variables

Ghenadie N. Mardari

Published Jan 1, 2018• 0 citations

Publisher

DOI: 10.1007/978-3-319-74971-6_12

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Bulletin of the American Physical SocietyOct 22, 20160 citations

It is generally assumed that {\em local realism} represented by a noncontextual and local hidden-variables model in

d=4

such as the one used by Bell always gives rise to CHSH inequality

|\langle B\rangle|\leq 2

. On the other hand, the contraposition of Gisin's theorem states that the inequality

|\langle B\rangle|\leq 2

for arbitrary parameters implies (pure) separable quantum states. The fact that local realism can describe only pure separable quantum states is naturally established in hidden-variables models, and it is quantified by

G({\bf a},{\bf b})= 4[\langle ψ|P({\bf a})\otimes P({\bf b})|ψ\rangle-\langle ψ|P({\bf a})\otimes{\bf 1}|ψ\rangle\langle ψ|{\bf 1}\otimes P({\bf b})|ψ\rangle]=0

for any two projection operators

P({\bf a})

and

P({\bf b})

. The test of local realism by the deviation of

G({\bf a},{\bf b})

from

G({\bf a},{\bf b})=0

is shown to be very efficient using the past experimental setup of Aspect and his collaborators in 1981.

\eta _c\rightarrow \varLambda {\bar{\varLambda }}

ηc→ΛΛ¯ and

\chi _{c0} \rightarrow \varLambda {\bar{\varLambda }}

χc0→ΛΛ¯ to test our inequalities, and show that their violations are likely to be observed with the data already collected in BESIII.