Optimal inequalities for state-independent contextuality with imperfect devices

Costantino Budroni

Piotr Badziąg, Ingemar Bengtsson, Adán Cabello +1 more

Matthias Kleinmann, Costantino Budroni, Jan-Åke Larsson +2 more

Contextuality is a natural generalization of nonlocality which does not need composite systems or spacelike separation and offers a wider spectrum of interesting phenomena. Most notably, in quantum mechanics there exist scenarios where the contextual behavior is independent of the quantum state. We show that the quest for an optimal inequality separating quantum from classical noncontextual correlations in a state-independent manner admits an exact solution, as it can be formulated as a linear program. We introduce the noncontextuality polytope as a generalization of the locality polytope and apply our method to identify two different tight optimal inequalities for the most fundamental quantum scenario with state-independent contextuality.

Junior R. Gonzales-Ureta, Ana Predojević, Adán Cabello

Bell inequalities that allow for the simultaneous observation of Bell nonlocality and Kochen-Specker contextuality are derived. These inequalities are shown to be maximally robust to either noise or detection inefficiency.

Otfried Gühne, Costantino Budroni, Adán Cabello +2 more

We show that the phenomenon of quantum contextuality can be used to certify lower bounds on the dimension accessed by the measurement devices. To prove this, we derive bounds for different dimensions and scenarios of the simplest noncontextuality inequalities. Some of the resulting dimension witnesses work independently of the prepared quantum state. Our constructions are robust against noise and imperfections, and we show that a recent experiment can be viewed as an implementation of a state-independent quantum dimension witness.

Raymond Lal