1. Effect of inelastic scattering on spin entanglement detection Elsa Prada Pablo San-Jose Karlsruhe University 27 August-1 September 2006 Keszthely, Lake Balaton, Hungary P. San-Jose and E. Prada, PRB 74, 045305 (2006)

2. Outline Beam splitter → entanglement detector Inelastic scattering (Technique: conserving voltage probe + entanglement) Shot noise measurements Higher order cumulants Conclusions

3. Beam splitter entanglement detector J.C. Egues, G. Burkard and D. Loss, PRL 89, 176401 (2002) Classical statistical mixture Singlet spin-entangled Triplet spin-entangled Pauli blocking mechanism

4. Inelastic scattering P. San-Jose and E. Prada, PRB 74, 045305 (2006) Model for inelastic scattering: Phenomenological voltage probe (Büttiker’86-’88) Conserving voltage probe (CVP) (Beenakker,Büttiker’92) Conserving voltage probe + General incoming non-locally correlated states Our technique Traditionally Langevin description of current fluctuations

5. Results: shot noise measurements T=1/2 T B =1 For  =0: easy to distinguish! For  =1: S s =S t =S m For singlet and mixed states: cosine-type dependence If T B <1… Triplet: easily detectable by its θ independence!

6. Robust entanglement detection scheme T=1/2 θ=0 If  is unknown… …it works for inelastic probabilities up to 50%

7. Higher order cumulants Concerning entanglement detection: skewness does not provide further information than noise

8. Conclusions Effect of inelastic scattering on entanglement detection through a beam splitter geometry Entanglement detection through shot noise remains possible for imperfect beam-splitter under inelastic scattering probabilities up to 50% Higher order cumulants do not give us more information We develop a way to implement current conservation in voltage probe setups when the incoming currents are nonlocally spin correlated P. San-Jose and E. Prada, PRB 74, 045305 (2006)

9. Generating function of the Levitov-Lee-Lesovik formulation of the FCS Our technique for CVP & entanglement Zero frequency limit of all current cumulants Localized wave packet representation → time-resolved technique Sequential scattering approach → valid in the long time limit Memory of probe’s excess charge through |Q> counter In accordance with Langevin description of current fluctuations