Maximal nonlocality from maximal entanglement and mutually unbiased bases, and self-testing of two-qutrit quantum systems

Understand

Bell inequalities are an important tool in device-independent quantum information processing because their violation can serve as a certificate of relevant quantum properties.

• Probably the best known example of a Bell inequality is due to Clauser, Horne, Shimony and Holt (CHSH), which is defined in the simplest scenario involving two dichotomic measurements and whose all key properties are well understood.
• There have been many attempts to generalise the CHSH Bell inequality to higher-dimensional quantum systems, however, for most of them the maximal quantum violation---the key quantity for most device-independent applications---remains unknown.
• On the other hand, the constructions for which the maximal quantum violation can be computed, do not preserve the natural property of the CHSH inequality, namely, that the maximal quantum violation is achieved by the maximally entangled state and measurements corresponding to mutually unbiased bases.