Any classical mediator, modeled as a commutative unital C*-algebra, cannot generate entanglement between two initially independent quantum systems, generalizing prior finite-dimensional no-go results to infinite dimensions.
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abstract
Models of quantum-classical interactions fall into two classes: those which allow the generation of quantum entanglement via a classical mediator (such as gravity), and those which do not. Marconato and Marletto have recently sought to distinguish between these classes by claiming that known members of the first class (based on the configuration-ensemble formalism introduced by us) fail to model the mediator as a 'classical' system, and are nonlocal. We explicitly show that this claim is incorrect, and expose a large number of errors and misconceptions in their reasoning. We also point to a very simple and transparent example of the generation of entanglement between two qubits via a classical bit. It follows that there are models permitting the generation of entanglement via quantum-classical interactions that lie outside the remit of the theorem cited by Marconato and Marletto. We clarify the reasons for the limited applicability of various no-go theorems for entanglement generation.
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Gravity-mediated entanglement via infinite-dimensional systems
Any classical mediator, modeled as a commutative unital C*-algebra, cannot generate entanglement between two initially independent quantum systems, generalizing prior finite-dimensional no-go results to infinite dimensions.