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arXiv · 1609.06114

Better local hidden variable models for two-qubit Werner states and an upper bound on the Grothendieck constant $K_G(3)$

Flavien Hirsch·Marco Túlio Quintino·Tamás Vértesi·Miguel Navascués·Nicolas Brunner
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Abstract

We consider the problem of reproducing the correlations obtained by arbitrary local projective measurements on the two-qubit Werner state $ρ= v |ψ_- > <ψ_- | + (1- v ) \frac{1}{4}$ via a local hidden variable (LHV) model, where $|ψ_- >$ denotes the singlet state. We show analytically that these correlations are local for $ v = 999\times689\times{10^{-6}}$ $\cos^4(π/50) \simeq 0.6829$. In turn, as this problem is closely related to a purely mathematical one formulated by Grothendieck, our result implies a new bound on the Grothendieck constant $K_G(3) \leq 1/v \simeq 1.4644$. We also present a LHV model for reproducing the statistics of arbitrary POVMs on the Werner state for $v \simeq 0.4553$. The techniques we develop can be adapted to construct LHV models for other entangled states, as well as bounding other Grothendieck constants.

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Flavien Hirsch, Marco Túlio Quintino, Tamás Vértesi, Miguel Navascués, Nicolas Brunner. 2017-04-14. Better local hidden variable models for two-qubit Werner states and an upper bound on the Grothendieck constant $K_G(3)$. https://doi.org/10.22331/q-2017-04-25-3

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