Entanglement and the factorization-approximation

Details Entanglement and the factorization-approximation Entanglement and the factorization-approximation

2001-09-27

arxiv.org/abs/quant-ph/0109140v1

Eur. Phys J. D 17, 385-393 (2001)

Physics

Quantum Physics

Accepted for publication in European Physical Journal D

Scientific paper

10.1007/s100530170012

For a bi-partite quantum system defined in a finite dimensional Hilbert space we investigate in what sense entanglement change and interactions imply each other. For this purpose we introduce an entanglement operator, which is then shown to represent a non-conserved property for any bi-partite system and any type of interaction. This general relation does not exclude the existence of special initial product states, for which the entanglement remains small over some period of time, despite interactions. For this case we derive an approximation to the full Schroedinger equation, which allows the treatment of the composite systems in terms of product states. The induced error is estimated. In this factorization-approximation one subsystem appears as an effective potential for the other. A pertinent example is the Jaynes-Cummings model, which then reduces to the semi-classical rotating wave approximation.

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