arXiv:2303.10157 · Physical Review A

Identifying primes from entanglement dynamics

A. L. M. Southier, Léa Ferreira dos Santos, P. H. Souto Ribeiro, A. D. Ribeiro

Published Oct 4, 2023• 5 citations

Abstract

The distribution of primes over the set of natural numbers is a fascinating subject closely related to topics that range from the fundamental problem of factorization to applications in cryptography. Despite numerous efforts, efficient methods to locate huge primes are still under investigation. Here, we present an alternative approach to identifying prime numbers that is based on the evolution of the linear entanglement entropy. Specifically, we show that a singular behavior in the amplitudes of the Fourier series of this entropy is associated with prime numbers. We also discuss how this intriguing connection between primes and entanglement could be experimentally implemented using existing optical devices, and examine a possible relationship between our results and the zeros of the Riemann zeta function.

DOI: 10.1103/physreva.108.042404

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