Biased Random Number Generator Based on Bell's Theorem**Supported by the National Natural Science Foundation of China under Grant Nos 61378011, U1204616 and 11447143, the Program for Science and Technology Innovation Talents in Universities of Henan Province under Grant No 2012HASTIT028, and the Program for Science and Technology Innovation Research Team in University of Henan Province under Grant No 13IRTSTHN020.

Abstract

We propose a biased random number generation protocol whose randomness is based on the violation of the Clauser–Horne inequality. Non-maximally entangled state is used to maximize the Bell violation. Due to the rotational asymmetry of the quantum state, the ratio of 0s to 1s varies with the measurement bases. The experimental partners can then use their measurement outcomes to generate the biased random bit string. The bias of their bit string can be adjusted by altering their choices of measurement bases. When this protocol is implemented in a device-independent way, we show that the bias of the bit string can still be ensured under the collective attack.