Photonic ternary quantum random number generators

Abstract

We construct a class of three-dimensional photonic quantum random number generators (QRNGs) and prove that each of them generates maximally unpredictable digits via measurements that are robust to errors. This shows that every sequence generated is strongly incomputable; hence its quality is provably better than that of every pseudo-random sequence. These results suggest that incomputability in physics is real and practically applicable. Finally, we present photonic implementations of three-dimensional QRNGs and discuss device independence.

Binary quantum random number generator based on value indefinite observables

“…Finally, using the Eigenstate principle and Theorem 5.6 in 14 , we deduce that the QRNG described above generates maximally unpredictable binary random digits.…”

“…This section introduces the physical principles and assumptions on which the notion of being "better than any PRNG" operates 8,13,14 . We then proceed to an explicit example based on a configuration of observables that realizes a QRNG according to these principles.…”

“…Eigenstate principle, if a quantum system is prepared in the state |ψ� , then the projection observable P ψ is value definite, then the projection observable P φ is value indefinite. Furthermore, in 14 , it was proved that given every probability distribution (p 1 , p 2 , p 3 ) ( i p i = 1 and 0 ≤ p i < 1 ), a value indefinite quantum state can be constructed which, by a universal measurement, produces the outcomes with probabilities p i .…”

“…By changing the input quantum state |a� = 0, 1, 0 T to |a� = 1, 0, 0 T and using the measurement (1) we obtain ternary quantum random numbers 0,1,2 generated with with probabilities 1/2, 1/4, 1/4, respectively, hence "genuine" ternary sequences. As many current applications require random binary sequences, in 14 , the computable alphabetic morphism ϕ : {0, 1, 2} → {0, 1}…”

Binary Quantum Random Number Generator Based on Value Indefinite Observables

“…All quantum random number generators, which rely on measuring value-indefinite observables [1][2][3] are three-dimensional. This is because the Kochen-Specker Theorem [4] is false in dimension two.…”