Entanglement and the factorization-approximation
Institut für Theoretische Physik, Universität Stuttgart, Pfaffenwaldring 57, 70550 Stuttgart, Germany
Published online: 15 December 2001
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 Schrödinger-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.
PACS: 03.65.Yz – Decoherence; open systems; quantum statistical methods / 42.50.Ct – Quantum description of interaction of light and matter; related experiments / 03.65.Ud – Entanglement and quantum nonlocality (e.g. EPR paradox, Bell's inequalities, GHZ states, etc.)
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2001