Randomness 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 [1], [2], 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 [3]. 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 [4] 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.

[1] J. Bouda, M. Pawlowski, M. Pivoluska, M. Plesch, Device-independent randomness extraction for arbitrarily weak min-entropy source , Phys. Rev. A 90, 032313 (2014). [2] 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). [3] 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). [4] 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).
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