Assessing the Intrinsic Randomness of Quantum States and Measurements

In this talk, we begin by introducing a general framework for quantifying the intrinsic quantum randomness. This framework allows us to compute the maximum guessing power of an eavesdropper, while fully accounting for the possibility that they may share classical or quantum correlations with the input state or even with the measurement itself. We then compute the intrinsic randomness of a mixed state and identify the measurements that optimize this quantity. Next, we derive the randomness generated by noisy measurements, along with the corresponding optimal states. Finally, we show that the simultaneous presence of noise in both the state and the measurement can significantly enhance the eavesdropper’s ability to guess the outcomes.