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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?. C.F. Roos et al

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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? 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: Schmidt diagonal basis: Separable Entangled Maximally entangled

  5. L.O.C.C Quantifying Entanglement  Entanglement Monotone  Concurrence

  6. → Mixed State Entanglement

  7. Time evolution under decoherence? 1-No measurement A B A B Env Env

  8. A B Env A B A B Env Env Time evolution under decoherence? 2-Continuous monitoring of Env. Run 1 Run N

  9. In general: Is there a way to monitor the environment such that

  10. A B E Model for : Markovian evolution

  11. Alternative: Quantum Trajectories Arbitrary choice of jump operators Jk under the constraint:

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

  13. A B A B Optimizing Measurement Setup Experimentally, "changing the unraveling" means changing the way of monitoring environment: Jump operators With a beam splitter:

  14. Zero temperature environment Initial state:

  15. CNOT + dephasing Jumps:

  16. 3 partite system Initial state: Jump operators (dephasing):

  17. Infinite temperature environment Initial state:

  18. Conclusion • We propose a characterization of entanglement dynamics from individualexperimental realizations. • We conjecture that there exists an optimal experimental setup which gives the correct 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? • Systematic method? Other kinds of unraveling (Q.S.D.)?

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