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Exploring Entanglement Dynamics in Shaking Out Theory for Quantum Systems

This forum discusses entanglement dynamics in quantum systems, focusing on separable and entangled states. It explores the relevance of entanglement to theoretical predictions like the Dynamical Casimir Effect (DCE) and Bogoliubov Transformations in Quantum Field Theory (QFT). Gaussian states and symplectic matrices are used to represent transformations in continuous variable systems. Various measures like Negativity and Von Neumann entropy quantify entanglement generation, showing linear growth and periodic behavior. The potential applications of entanglement generation in DCE, Quantum Information (QI), and particle creation are also discussed, along with challenges related to dissipative systems and different particles.

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Exploring Entanglement Dynamics in Shaking Out Theory for Quantum Systems

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  1. Young Theorists Forum Durham 2011 “Shaking Out” Entanglement Antony Lee University of Nottingham D.E.Bruschi, A.Dragan, I.Fuentes & J. Louko

  2. Entanglement • Definition: Separable • A state is said to be separable with respect to two partitions if it can be written as the tensor product of two independent states • Definition: Entangled • If a state cannot be written as separable then it is entangled • Relevance • Way of verifying theoretical predictions • Can be linked to the Dynamical Casimireffect (DCE)

  3. Bogoliubov Transformations • QFT • States of fields • Two mode truncation • Validity • Very accurate for low accelerations • Physically reasonable

  4. Basic Trajectories

  5. “Shaking”

  6. Continuous Variables • Definition • Any system whose observables have a continuous spectrum • Collections of molecules, Atoms, lasers etc. • Basics • Any Gaussian state is represented by its first and second moment expectation values

  7. Gaussian States • Relevance • Represent the state and the transformations using symplectic matrices • Truncated transformation represented as a change of basis • Multiple “shakes” represented the repeated action of the symplectic transformations i.e.

  8. Results • Quantifying entanglement • Many different measures, Negativity, Logarithmic Negativity, Von Neumann entropy • Periodic structure • Entanglement generation rises and lowers • Linear growth • For special fixed parameters • there is unbounded generation of entanglement

  9. Conclusions • Entanglement generation • High degrees of entanglement • Use for DCE • Linked to particle creation therefore temperature • Use for QI • Resource of strongly entangled pairs • Further problems • Dissipative systems, different particles

  10. Thank You & Questions?

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