Can entanglement be mediated by a Koopmanian system?

TL;DR

This paper investigates whether a classical system modeled via Koopman dynamics can mediate entanglement between two quantum bits, concluding it cannot, which has implications for semi-classical quantum gravity models.

Contribution

It introduces a method to couple Koopmanian classical systems with quantum bits and proves such coupling cannot generate entanglement, highlighting fundamental limitations of hybrid quantum-classical systems.

Findings

Coupling via Koopmanian systems does not produce entanglement.

Hybrid systems violate conservation laws as expected.

Implications for semi-classical quantum gravity models.

Abstract

We present a method for coupling a Koopmanian classical system to two quantum bits to mediate an interaction between them. We then prove that the resulting dynamics can never lead to entanglement between the two qubits. Even though the total system of two qubits and the Koopmanian classical system are described with the full quantum formalism, we show that their composite system violates exact conservation laws as expected for a hybrid quantum-classical system. We finally discuss the implications for semi-classical treatments of quantum gravity.