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.

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Presentation transcript:

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

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, (2004)

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

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

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- M is convex Example: concurrence –Tr

Pure state / Mixture Convex Roof: Decomposition of density operator: How to define the Entanglement measure? Not Unique

Time evolution under decoherence?

Model: Markovian evolution

Quantifying Entanglement Numerics Time t

Alternative: Quantum Trajectories

Averaged Entanglement ???

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

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

Zero temperature environment Initial state: M

Infinite temperature environment Initial state: M

CNOT + dephasing Jumps: M Adding a unitary evolution

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

Conclusion We propose a characterization of entanglement dynamics from individual experimental 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.

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