QUAntum SAfe Randomness

Unbounded randomness from uncharacterized sources

Marco Avesani, Hamid Tebyanian, Paolo Villoresi, Giuseppe Vallone
Manuscript available on: [arXiv:2010.05798]
Experimental setup. Source (red) is untrusted, measurement devices (green) are trusted

Randomness is a central feature of quantum mechanics and an invaluable resource for both classical and quantum technologies. The generation and certification of randomness with minimal assumptions is of central interest for both theoretical physics and for security applications. In this area, Device-Independent and Semi-Device-Independent protocols are actively studied in order to increase both security and generation rates.

In these scenarios, randomness is typically certified using projective measurements, and the amount of certified randomness is limited by the dimension of the measured quantum system, thus limiting the final generation rate.

Min-entropy for the 10-outcome

In this work, we propose a new Source-Device-Independent protocol, based on Positive Operator Valued Measurement (POVM), which can arbitrarily increase the number of certified bits for any fixed dimension. This protocol demonstrates for the first time that unbounded randomness can be generated in finite-dimension systems with Semi-DI protocols.

We derive tight lower-bound on the quantum conditional min-entropy using only the POVM structure and the experimental expectation values, taking into account the quantum side-information. We have developed both numerical and analytical methods to estimate the extractable randomness for different measurement configurations. Finally, we experimentally demonstrate our method with a compact and simple photonic setup that employs polarization-encoded qubits and POVM up to 6 outcomes.


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