2017

Quantum measurement incompatibility does not imply Bell nonlocality

Hirsch, Flavien, Quintino, Marco Túlio, Brunner, Nicolas

Understand

We discuss the connection between the incompatibility of quantum measurements, as captured by the notion of joint measurability, and the violation of Bell inequalities.

Specifically, we present explicitly a given a set of non jointly measurable POVMs $\mathcal{M}_A$ with the following property.
Considering a bipartite Bell test where Alice uses $\mathcal{M}_A$, then for any possible shared entangled state $\rho$ and any set of (possibly infinitely many) POVMs $\mathcal{N}_B$ performed by Bob, the resulting statistics admits a local model, and can thus never violate any Bell inequality.
This shows that quantum measurement incompatibility does not imply Bell nonlocality in general.

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Then

M. Túlio Quintino, J. Bowles, F. Hirsch, and N. Brunner, “Incompatible quantum measurements admitting a local hidden variable model,” ArXiv e-prints
Original
2015
Later among the works it cites.
D. Cavalcanti and P. Skrzypczyk, “Quantum steering: a short review with focus on semidefinite programming,” ArXiv e-prints
Original
2016
Later among the works it cites.
J. Bowles, F. Hirsch, M. T. Quintino, and N. Brunner, “Sufficient criterion for guaranteeing that a two-qubit state is unsteerable,” Phys. Rev. A
Original
2016
Later among the works it cites.
F. Hirsch, M. T. Quintino, T. Vértesi, M. F. Pusey, and N. Brunner, “Algorithmic Construction of Local Hidden Variable Models for Entangled Quantum States,” Phys. Rev. Lett
Original
2016
Later among the works it cites.
D. Cavalcanti, L. Guerini, R. Rabelo, and P. Skrzypczyk, “General Method for Constructing Local Hidden Variable Models for Entangled Quantum States,” Phys. Rev. Lett
Original
2016
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S. Brierley, M. Navascues, and T. Vertesi, “Convex separation from convex optimization for large-scale problems,” ArXiv e-prints
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2016
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M. Oszmaniec, L. Guerini, P. Wittek, and A. Acín, “Simulating positive-operator-valued measures with projective measurements,” ArXiv e-prints
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2016
Later among the works it cites.
F. Hirsch, M. T. Quintino, T. Vértesi, M. Navascués, and N. Brunner, “Better local hidden variable models for two-qubit Werner states and an upper bound on the Grothendieck constant K G ( 3 ) K_{G}(3) ,” Quantum
2017
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L. Guerini, J. Bavaresco, M. Terra Cunha, and A. Acín, “Operational framework for quantum measurement simulability,” ArXiv e-prints
Original
2017
Closest in time.
B. Erika and T. Vértesi, “Measurement incompatibility does not give rise to Bell violation in general,” ArXiv e-prints
Original
2017
Closest in time.
J. Bavaresco, M. Túlio Quintino, L. Guerini, T. O. Maciel, D. Cavalcanti, and M. Terra Cunha, “Most incompatible measurements for robust steering tests,” ArXiv e-prints
Original
2017
Closest in time.

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