2015

Algorithmic construction of local hidden variable models for entangled quantum states

Hirsch, Flavien, Quintino, Marco Túlio, Vértesi, Tamás et al.

Understand

Constructing local hidden variable (LHV) models for entangled quantum states is challenging, as the model should reproduce quantum predictions for all possible local measurements.

Here we present a simple method for building LHV models, applicable to general entangled states, which consists in verifying that the statistics resulting from a finite set of measurements is local, a much simpler problem.
This leads to a sequence of tests which, in the limit, fully capture the set of quantum states admitting a LHV model.
Similar methods are developed for constructing local hidden state models.

Built on

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Similar

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Note that χ \chi does not need to be positive, but should only define a valid assemblage (Protocol 1), or a valid probability distribution (Protocol 2), for the considered sets of measurements { M a | x } \{M_{a|x}\} (and { M b | y } \{M_{b|y}\} )
Cited in the paper.

Then

J. Bowles, T. Vértesi, M. T. Quintino, and N. Brunner, “One-way Einstein-Podolsky-Rosen Steering,” Phys. Rev. Lett. 112
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2015
Closest in time.
M. T. Quintino, T. Vértesi, D. Cavalcanti, R. Augusiak, M. Demianowicz, A. Acín, and N. Brunner, “Inequivalence of entanglement, steering, and Bell nonlocality for general measurements,” Phys. Rev. A 92
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J. Bowles, F. Hirsch, M. T. Quintino, and N. Brunner, “Local Hidden Variable Models for Entangled Quantum States Using Finite Shared Randomness,” Phys. Rev. Lett. 114
2015
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J. Bowles, F. Hirsch, M. T. Quintino, and N. Brunner, Phys. Rev. A 93
2016
Closest in time.

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