Looking for symmetric Bell inequalities
نویسندگان
چکیده
Finding all Bell inequalities for a given number of parties, measurement settings and measurement outcomes is in general a computationally hard task. We show that all Bell inequalities which are symmetric under the exchange of parties can be found by examining a symmetrized polytope which is simpler than the full Bell polytope. As an illustration of our method, we generate 238 885 new Bell inequalities and 1085 new Svetlichny inequalities. We find, in particular, facet inequalities for Bell experiments involving two parties and two measurement settings that are not of the Collins–Gisin–Linden–Massar–Popescu type. BANCAL, Jean-Daniel, GISIN, Nicolas, PIRONIO, Stefano. Looking for symmetric Bell inequalities. Journal of Physics. A, Mathematical and Theoretical, 2010, vol. 43, no. 38, p.
منابع مشابه
Bell Inequalities and Entanglement Witnesses Using Two-Body Correlations
It has been shown that there exist Bell inequalities constructed from symmetric oneand two-body correlations that are violated by certain quantum states involving any number of particles. However, the properties of such Bell inequalities have not been completely characterised. In this study, we determine the behaviour of various classes of entangled states with respect to these inequalities. It...
متن کاملEquivalence between Bell inequalities and quantum Minority game
We show that, for a continuous set of entangled four-partite states, the task of maximizing the payoff in the symmetric-strategy four-player quantum Minority game is equivalent to maximizing the violation of a four-particle Bell inequality with each observer choosing the same set of two dichotomic observables. We conclude the existence of direct correspondences between (i) the payoff rule and B...
متن کاملCHSH type Bell inequalities involving a party with two or three local binary settings
We construct a simple algorithm to generate any CHSH type Bell inequality involving a party with two local binary measurements from two CHSH type inequalities without this party. The algorithm readily generalizes to situations, where the additional observer uses three measurement settings. There, each inequality involving the additional party is constructed from three inequalities with this par...
متن کاملSymmetric Rogers-Hölder's inequalities on diamond-α calculus
We present symmetric Rogers--Hölder's inequalities on time scales when $frac{1}{p}+frac{1}{q}+frac{1}{r}=0$ and $frac{r}{p}+frac{r}{q}$ is not necessarily equal to $1$ where $p,$ $q$ and $r$ are nonzero real numbers.
متن کاملPartial list of bipartite Bell inequalities with four binary settings
We give a partial list of 26 tight Bell inequalities for the case where Alice and Bob choose among four two-outcome measurements. All tight Bell inequalities with less settings are reviewed as well. For each inequality we compute numerically the maximal quantum violation, the resistance to noise and the minimal detection efficiency required for closing the detection loophole. Surprisingly, most...
متن کامل