Multipartite entanglement Characterization and applications

1. Multipartite entanglement Characterization and applications Mohamed Bourennane Physics Department, Stockholm University boure@physto.se

2. Plan Introduction Experimental generation of three and four photon polarization Entanglement Bell inequalities Entanglement Witness Decoherence free quantum communication

3. Twopartite entanglement Quantum information: Qubit Two-qubit: Bell State Violation of Bell inequality  Entanglement But the no violation of Bell inequality ? Peres-Horodecki criterion: Positive Partial Transpose Applications in Quantum Information Processing: Quantum Cryptography: Quantum key Distribution Quantum Teleportation etc

4. Two photon polarization entanglement Bell State: Two photon polarization entangled state Spontaneous Parametric Down-Conversion

5. Four Qubits state Second order process in Spontaneous Parametric Down-Conversion

6. Four photon state Fourfold coincidences in 3 hours 4-5 fourfold coincidences/10 second

7. V = 92.29% ± 0.83% + Four Photon Quantum Correlations Polarization measurement operator Four-photon correlation function

8. S = 1.666 ± 0.028 (4) Bell Inequality Bell inequality summarizes all possible local realistic constraints on the correlation function for the case of each local observer measuring the polarizations along two alernative directions 16 local directions Violation of four photon Bell inequality Eibl et al, PRL 90 (2003) 200403.

9. Three qubit W state TH=RV=2/3

10. Three Photon W state

11. V = 86.4% ± 1.9% (100) V = 48.1% ± 2.9% (66) + + Three Photon Quantum Correlation

12. S ≤2 M A-B-C S = 3 M S ≤2√2 M AB-C Mermin Inequality Theory Experiment S = 2.468 ± 0.063 M Eibl et al, PRL 92 (2004) 077901.

13. A operator is called Entanglement witness detecting the entangled state iff Witnessing Multipartite Entanglement A n party state is Genuine multipartite entangled all the parties are entangled with each other Biseparable m parties are entangled with each other but not with the rest Three qubits: Three different inequivalent classes under SLOCC (GHZ and W) Separable (product states) Biseparables

14. Local decomposition Decomposition into local von Neumann (or projective) measurement Optimal local decomposition when K minimal

15. Threepartite Entanglement Witness Experimental detection of genuine threepartite entangement

16. Fourpartite Entanglement Witness Experimental detection of genuine fourpartite entanglement Bourennane et al, PRL 92 (2004) 087902.

17. Decoherence-free Superpositions: Very fragile Unwanted coupling with the environment Noise in communication Error in computation Several Stategeies to scope with decoherence Weak interaction: redundancy added, active quantum error correction codes Symmetric interaction: Encoding with invariant states under the interaction A particular relevant symmetry arises when the environment couples identically to all the qubits : Collective noise The smallest DFS is spanned by two four qubit states where

18. DFS states Four photon polarization entangled states

19. DFS States Half and quarter wave plates at 13.5 and 59 (A): (B): (C): (D):

20. Distinguishability DFS States Distinguishability with local measurements Photons a and b in {H,V} basis Photons c and d in {+45,-45} (A): (B): (C): (D):

21. Encoding in DFS Quantum information encoding Bourennane et al, PRL 92 (2004) 107901.

22. Conclusion • Experimental generation of three and four • photon polarization Entanglement • Multipartite Bell inequalities • Detection of Multipartite Entanglement • with the witness method • Decoherence free Quantum communication