Qubit from the classical collision entropy

TL;DR

This paper derives a qubit and its dynamics from a discrete classical framework based on collision entropy, avoiding the need for Hilbert space formalism, thus providing a new foundational perspective.

Contribution

It introduces a novel derivation of qubits directly from classical discrete dynamics and collision entropy, bypassing traditional quantum postulates.

Findings

Qubit dynamics can be obtained from classical collision entropy conservation.

Hilbert space formalism can be inferred but is not necessary for quantum description.

Provides a new classical-based foundation for quantum mechanics.

Abstract

An orthodox formulation of quantum mechanics relies on a set of postulates in Hilbert space supplemented with rules to connect it with classical mechanics such as quantisation techniques, correspondence principle, etc. Here we deduce a qubit and its dynamics straightforwardly from a discrete deterministic dynamics and conservation of the classical collision entropy. No Hilbert space is required although it can be inferred from this approach if necessary.