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Unraveling Entanglement

Unraveling Entanglement. O. Brodier M. Busse, C. Viviescas, A. R. R. Carvalho, A. Buchleitner M.P.I.P.K.S. N öthnitzer Str. 38, D-01187 DRESDEN, ALLEMAGNE. Problematic. How to characterize and understand dynamics of entanglement in an open system? Understand what makes a state robust.

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Unraveling Entanglement

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  1. Unraveling Entanglement O. Brodier M. Busse, C. Viviescas, A. R. R. Carvalho, A. Buchleitner M.P.I.P.K.S. Nöthnitzer Str. 38, D-01187 DRESDEN, ALLEMAGNE

  2. Problematic How to characterize and understand dynamics of entanglement in an open system? Understand what makes a state robust. C.F. Roos et al P.R.L. 92, 220402 (2004)

  3. Plan • Definitions: entanglement measures. • Context and Methods: Markovian open system, Quantum trajectories. • Application: evaluation of entanglement measures. • Results

  4. Definition of Entanglement • A system is a tensor product of two subsystems: • It is separable, with respect to A and B, if one can write: in the pure case for a mixture • Otherwise it is entangled

  5. Quantifying Entanglement • Entanglement Monotone: 1-M(ρ)≥0, equality if ρ is separable 2-M(ρ)does not grow under Local Operation and Classical Communication 3-Mis convex • Example: concurrence –Tr

  6. Pure state / Mixture • Decomposition of density operator: • How to define the Entanglement measure? • Convex Roof: NotUnique

  7. Time evolution under decoherence?

  8. Model: Markovian evolution

  9. Quantifying Entanglement Time t Numerics

  10. Alternative: Quantum Trajectories

  11. Averaged Entanglement ???

  12. Optimizing Unraveling • The master equation is invariant up to linear & unitary transform of the jump operators: With unitary U • The average over trajectories is not invariant → it can be optimized

  13. Optimizing Measurement Setup Experimentally, changing the unraveling means changing the Experimental setup: Beam Splitter Unitary transform

  14. Zero temperature environment Initial state: M

  15. Infinite temperature environment Initial state: M

  16. CNOT + dephasing Adding a unitary evolution Jumps: M

  17. 3 partite system Initial state: Jump operators (dephasing): M

  18. Conclusion • We propose a characterization of entanglement dynamics from individualexperimental realizations. • We conjecture that there exists an optimal experimental setup which gives the exact measure. • Alternative for step by step optimization. • Mathematical proof for small times in two-partite systems.

  19. Perspectives • Does-it always work (multipartite)? Then why? • Systematical method? Other kinds of unraveling (Q.S.D.)?

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