Interference in Complex Canonical Variables Is Not Quantum

Journal article

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 complex classical Hamiltonian dynamics, we show that the resulting system is still not a proper qubit. The reason for this 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 difficulties faced by hybrid quantum–classical models in accounting for the full range of behaviour of quantum systems.

Authors: Marletto, C; Vedral, V

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: MDPI
• Journal: Quantum Reports
• Volume: 7
• Issue: 3
• Pages: 40
• Article number: 40
• Publication date: 2025-09-09
• Acceptance date: 2025-09-02
• DOI: 10.3390/quantum7030040
• EISSN: 2624-960X
• ISSN: 2624-960X
• Language: English
• Keywords: quantum information; quantum foundations; quantum-classical models