Semi-device-independent random-number expansion without entanglement

By testing the classical correlation violation between two systems, true random numbers can be generated and certified without applying classical statistical method. In this work, we propose a true random-number expansion protocol without entanglement, where the randomness can be guaranteed only by the two-dimensional quantum witness violation. Furthermore, we only assume that the dimensionality of the system used in the protocol has a tight bound, and the whole protocol can be regarded as a semi-device-independent black-box scenario. Compared with the device-independent random-number expansion protocol based on entanglement, our protocol is much easier to implement and test.

Figure 1

Semi-device-independent random-number expansion protocol. The protocol requires the state preparation black box and the state measurement black box, respectively. Both of the black boxes are in the same safe area.

Figure 2

The relationship between the two-dimensional quantum witness and the the min-entropy bound. The min-entropy starts at zero in the two-dimensional classical witness case; systems that violate the two-dimensional quantum witness 2.64 have a positive min-entropy.