RandomnessRandomness is an integral part of many scientific fields, which include quantum mechanics or information theory. In many applications, like numerical simulations or cryptography, just to name a few, free randomness is desired due to the fact that a wide range of results is based on it. In practice, however, usually only weak sources of randomness are available. Although amplifying the randomness of a single weak source is unattainable in classical information theory, it becomes possible, if the no-signaling principle is assumed and quantum-mechanical correlations (revealed operationally through the violation of Bell inequalities) are used.
KCIK researchers have contributed to the field by providing the proofs for device-independent randomness amplification protocols , , where the second one solves the problem of being trapped between two restrictive alternatives: the need for many devices or fragility to noise. The problem of randomness extraction is, at the same time, analyzed from another perspective – the perspective of practical experimental realization. The general analytical relationship between the maximal average guessing probability and dimension witness is given in . Finally, it is a fact that in finite time randomness cannot be amplified to the perfect one. This raises a question how protocols that require it behave when fed with weak randomness. In  the security of quantum key distribution is studied in this scenario.
In KCIK, the research concerning randomness is still in progress and develops in all mentioned directions.
 J. Bouda, M. Pawlowski, M. Pivoluska, M. Plesch, Device-independent randomness extraction for arbitrarily weak min-entropy source , Phys. Rev. A 90, 032313 (2014).  F. G.S.L. Brandão, R. Ramanathan, A. Grudka, K. Horodecki, M. Horodecki, P. Horodecki, T. Szarek, H. Wojewódka, Realistic noise-tolerant randomness amplification using finite number of devices , Nature Communications 7, Article number: 11345 (2016).  Hong-Wei Li, Zhen-Qiang Yin, M. Pawłowski, Guang-Can Guo, Zheng-Fu Han, Detection efficiency and noise in a semi-device-independent randomness-extraction protocol , Phys. Rev. A 91, 032305 (2015).  M. Huber, M. Pawłowski, Weak randomness in device independent quantum key distribution and the advantage of using high dimensional entanglement , Phys. Rev. A 88, 032309 (2013).