Natural Numbers and Quantum States in Fock Space

TL;DR

This paper explores representing natural numbers in various bases using quantum states in Fock space, introducing operators that encode number coefficients through quantum state transformations.

Contribution

It introduces multiboson and translation operators acting on Fock states to encode natural numbers in any base from a quantum perspective.

Findings

Operators successfully encode natural numbers in different bases.

Quantum states correspond uniquely to natural numbers across bases.

Framework bridges number theory and quantum state manipulation.

Abstract

We investigate the expression of natural numbers in any base from a quantum point of view. In particular, resorting to the one-to-one correspondence between natural numbers and Fock states, we construct a set of multiboson operators and a set of translation operators, whose action on the Fock states leads to the coefficients identifying a natural number in any base.