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? 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: Schmidt diagonal basis: Maximally entangled Entangled Separable

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

Mixed State Entanglement →

Theoretical point of view known No measurement

Time evolution of entanglement under decoherence? E E A B A B

Model for : Markovian evolution Lindblad equation: E A B

Experimental point of view: Continuous monitoring of environment

Time evolution of average ebtanglement under decoherence? Run 1 Run N E A B D D E A B D D Run 2 Run N-1 E A B D D

Quantum Trajectories (Monte Carlo) Arbitrary choice (unraveling) of jump operators J k under the constraint:

In general: Is there a way to monitor the environment such that A.R.R.Carvalho, M.Busse, O.B.,C.Viviescas, A.Buchleitner quant-ph/

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

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

Zero temperature environment Initial state:

CNOT + dephasing Jumps:

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

Infinite temperature environment Initial state:

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

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