Indistinguishability between quantum randomness and pseudo-randomness under efficiently calculable randomness measures

Abstract

We present a no-go theorem for the distinguishability between quantum random numbers (i.e., random numbers generated quantum mechanically) and pseudo-random numbers (i.e., random numbers generated algorithmically). The theorem states that one cannot distinguish these two types of random numbers if the quantum random numbers are efficiently classically simulatable and the randomness measure used for the distinction is efficiently computable. We derive this theorem by using the properties of cryptographic pseudo-random number generators, which are believed to exist in the field of cryptography. Our theorem is found to be consistent with the analyses on the actual data of quantum random numbers generated by the IBM Quantum and also those obtained in the Innsbruck experiment for the Bell test, where the degrees of randomness of these two set of quantum random numbers turn out to be essentially indistinguishable from those of the corresponding pseudo-random numbers. Previous observations on the algorithmic randomness of quantum random numbers are also discussed and reinterpreted in terms of our theorems and data analyses.

arXiv comment17 pages, 8 figures, 3 tables. title updated, minor revision

References in corpus (17)

• Experimental loophole-free violation of a Bell inequality using entangled electron spins separated by 1.3 km
• Advances in Quantum Cryptography
• Violation of Bell's inequality under strict Einstein locality conditions
• Significant-loophole-free test of Bell's theorem with entangled photons
• A strong loophole-free test of local realism
• Violation of Bell inequalities by photons more than 10 km apart
• Quantum Random Number Generators
• On the role of entanglement in quantum computational speed-up
• Bell violation with entangled photons, free of the fair-sampling assumption
• Event-Ready Bell Test Using Entangled Atoms Simultaneously Closing Detection and Locality Loopholes
• Cosmic Bell Test using Random Measurement Settings from High-Redshift Quasars
• Experimental Evidence of Quantum Randomness Incomputability
• Bell's inequality violation with spins in silicon
• On the non-randomness of maximum Lempel Ziv complexity sequences of finite size
• Experimentally Probing the Algorithmic Randomness and Incomputability of Quantum Randomness
• Kolmogorov complexity of sequences of random numbers generated in Bell's experiments
• How random are random numbers generated using photons?

Cited by in corpus (1)

• Evaluating Quantumness, Efficiency and Cost of Quantum Random Number Generators via Photon Statistics