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
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)
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:
• It is separable, with respect to A and B, if one can
write:
in the pure case
for a mixture
• Otherwise it is entangled
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
• Decomposition of density operator:
• How to define the Entanglement measure?
Not Unique
• Convex Roof:
Time evolution under decoherence?
Model: Markovian evolution
Quantifying Entanglement
Time t
Numerics
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
Experimentally, changing the unraveling means changing the
Experimental setup:
Beam Splitter
Unitary transform
Zero temperature environment
Initial state:
M
Infinite temperature environment
Initial state:
M
CNOT + dephasing
Adding a unitary evolution
Jumps:
M
3 partite system
Initial state:
Jump operators (dephasing):
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.)?