Maximizing device-independent randomness from a Bell experiment by optimizing the measurement settings

The rates at which a user can generate device-independent quantum random numbers from a Bell-type experiment depend on the measurements that the user performs. By numerically optimizing over these measurements, we present lower bounds on the randomness generation rates for a family of two-qubit states composed from a mixture of partially entangled states and the completely mixed state. We also report on the randomness generation rates from a tomographic measurement. Interestingly in this case, the randomness generation rates are not monotonic functions of entanglement.