TY - JOUR
AB - 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)14 via a local hidden variable (LHV) model, where |ψ−⟩ denotes the singlet state. We show analytically that these correlations are local for v=999×689×10−6 cos2(π/50)≃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 KG(3)≤1/v≃1.4644. We also present a LHV model for reproducing the statistics of arbitrary POVMs on the Werner state for v≃0.4553. The techniques we develop can be adapted to construct LHV models for other entangled states, as well as bounding other Grothendieck constants.
AU - Hirsch, F.
AU - Quintino, M. T.
AU - Vértesi, T.
AU - Navascués, M.
AU - Brunner, N.
DA - 2017/04/25/
DO - 10.22331/q-2017-04-25-3
ET - 2017/10/09/
JF - Quantum
PY - 2017
SE - 2017/04/25/
SP - 3
TI - Better local hidden variable models for two-qubit Werner states and an upper bound on the Grothendieck constant KG(3)
UR - https://quantum-journal.org/papers/q-2017-04-25-3/
VL - 1
ER -