Interference in complex canonical variables is not quantum

TL;DR

This paper demonstrates that classical Hamiltonian models with complex variables can mimic quantum interference in a single qubit but cannot replicate true quantum entanglement or information processing capabilities.

Contribution

It shows that classical complex Hamiltonian dynamics cannot fully replicate quantum behavior, especially entanglement, highlighting limitations of hybrid models.

Findings

Classical complex Hamiltonian models can simulate quantum interference.

Such models cannot produce entanglement between qubits.

Hybrid models fail to capture the full quantum information processing.

Abstract

We formally represent the quantum interference of a single qubit embodied by a photon in the Mach-Zehnder interferometer using the classical Hamiltonian framework but with complex canonical variables. Although all operations on a single qubit can be formally expressed using the complex classical Hamiltonian dynamics, we show that the resulting system is still not a proper qubit. The reason is that it is not capable of getting entangled to another bona fide qubit and hence it does not have the information-processing capacity of a fully-fledged quantum system. This simple example powerfully illustrates the failure of all hybrid quantum-classical models in accounting for the full range of behaviour of even a single quantum bit.