For any qubit-qudit state under all projective measurements, an LHV model with outcome communication exists if and only if a standard LHV model without communication exists.
Better local hidden variable models for two-qubit Werner states and an upper bound on the Grothendieck constant $K_G(3)$
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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 $\rho = v |\psi_- > <\psi_- | + (1- v ) \frac{1}{4}$ via a local hidden variable (LHV) model, where $|\psi_- >$ denotes the singlet state. We show analytically that these correlations are local for $ v = 999\times689\times{10^{-6}}$ $\cos^4(\pi/50) \simeq 0.6829$. 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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Reviews paradigmatic entanglement quantifiers and state-of-the-art detection/certification methods, with emphasis on assumptions about states and measurements.
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For any qubit-qudit state under all projective measurements, an LHV model with outcome communication exists if and only if a standard LHV model without communication exists.
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Reviews paradigmatic entanglement quantifiers and state-of-the-art detection/certification methods, with emphasis on assumptions about states and measurements.