Homogenization of Bell inequalities

Abstract

A technique, which we call homogenization, is applied to transform CH-type Bell inequalities, which contain lower order correlations, into CHSH-type Bell inequalities, which are defined for highest order correlation functions. A homogenization leads to inequalities involving more settings, that is a choice of one more observable is possible for each party. We show that this technique preserves the tightness of Bell inequalities: a homogenization of a tight CH-type Bell inequality is still a tight CHSH-type Bell inequality. As an example we obtain $3\times 3\times 3$ CHSH-type Bell inequalities by homogenization of $2\times 2\times 2$ CH-type Bell inequalities derived by Sliwa in [Phys. Lett. A {\bf 317}, 165 (2003)].

References in corpus (13)

• Random Numbers Certified by Bell's Theorem
• Bell Inequalities for Graph States
• Lifting Bell inequalities
• Tight multipartite Bell's inequalities involving many measurement settings
• On the Relationship between Convex Bodies Related to Correlation Experiments with Dichotomic Observables
• Quantum nonlocality of four-qubit entangled states
• Two-setting Bell Inequalities for Graph States
• Two-Party Bell Inequalities Derived from Combinatorics via Triangular Elimination
• Mermin inequalities for perfect correlations
• Explicit form of correlation function three-settings tight Bell inequalities for three qubits
• Bell inequality for qubits based on the Cauchy-Schwarz inequality
• Extending Bell inequalities to more parties
• CHSH type Bell inequalities involving a party with two or three local binary settings

Cited by in corpus (3)

• Bound entanglement helps to reduce communication complexity
• Compact Bell inequalities for multipartite experiments
• Quantum Nonlocality Enhanced by Homogenization