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Entanglement Distribution Via Quantum Communication Anindita Banerjee Department of Physics

Entanglement Distribution Via Quantum Communication Anindita Banerjee Department of Physics Centre of Astroparticle Physics and Space Science Bose Institute. Basic Definitions Introduction Motivation Results. Outline. Entanglement. Source: perimeterinstitute.ca/videos/alice-and-bob.

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Entanglement Distribution Via Quantum Communication Anindita Banerjee Department of Physics

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  1. Entanglement Distribution Via Quantum Communication AninditaBanerjee Department of Physics Centre of Astroparticle Physics and Space Science Bose Institute

  2. Basic Definitions Introduction Motivation Results Outline

  3. Entanglement Source:perimeterinstitute.ca/videos/alice-and-bob

  4. Entanglement measures Trace norm is the sum of the absolute values of the eigen value of the density matrix Log Negativity: Partial transpose of the bipartite mixed state

  5. Dense Coding [Bennett, C.; Wiesner, S.  Phys. Rev. Lett. 69 (20): 2881 (1992)]. • Teleportation [C. H. Bennett et al., Phys. Rev. Lett. 70, 1895 (1993)]. Entanglement is a resource But ENTANGLEMENT is an EXPENSIVE Resource? Why is Entanglement a resource? We can implement global quantum operations by LOCC. Yes but our government will provide it FREE.

  6. Alice’s Lab Bob’s Lab QUANTUM CHANNEL A B Initial Entanglement between Alice’s Lab and Bob’s Lab =0 Alice sends entangled particle B to Bob A B Final entanglement is same as the communicated entanglement B A

  7. Theory: T.S. Cubitt, F. Verstraete, W. Dür, J.I. Cirac. "Separable States can be used to distribute entanglement". Physical Review Letters, 91, 037902 (2003). No entanglement is necessary to distribute entanglement C B A Experiment: Christina E. Vollmer et al., Experimental Entanglement Distribution by Separable States, Phys. Rev. Lett. 111, 230505 (2013).

  8. Alice’s Lab Bob’s Lab QUANTUM CHANNEL QUANTUM CHANNEL C C C A B (A vs BC)0 (AC vs B)=0 (C vs AB)=0

  9. Entanglement Distribution Direct Distribution Indirect Distribution C A A A B A B B B C A B

  10. Indirect Distribution protocol Initial Entanglement ( INITIAL ) = AC/B Communicated entanglement ( COM ) = AB/C Final Entanglement ( FINAL ) = A/BC Entanglement change = FINALINITIAL = A/BC AC/B COM non excessive excessive COM

  11. CASE 1 IS SUBJECTED TO PARAMETER q Alice Bob 1 2 3 4 5

  12. Initial Entanglement ( INITIAL ) = 12/345 Communicated entanglement ( COM ) = 3/1245 Final Entanglement ( FINAL ) = 123/45 Entanglement change COM Init FINAL INITIAL COM 123/45 12/345 3/1245 Log negativity q

  13. CASE 2 Alice Bob 3 1 2 4 5

  14. Initial Entanglement ( INITIAL ) = 3/1245 Communicated entanglement ( COM ) = 1/2345 Final Entanglement ( FINAL ) = 13/245 Entanglement change COM Init FINAL INITIAL COM 13/245 3/1345 1/2345 Log negativity q

  15. CASE 3 Alice Bob 2 3 1 4 5

  16. Initial Entanglement ( INITIAL ) = 2/1345 Communicated entanglement ( COM ) = 3/1245 Final Entanglement ( FINAL ) = 23/245 Entanglement change COM Init FINAL INITIAL COM 23/245 2/1345 3/1245 Log negativity q

  17. ? Increase ? Increase

  18. COLLABORATORS Somshubhro Bandyopadhyay Saronath Haldar Prasnjit Deb Tomasz Paterek Kavan Modi Margherita Zuppardo

  19. Thank you

  20. Absolutely Maximally Entangled state AME(n,d) is a pure state of n qudits in d dimension such that every bipartition of the system is strictly maximally entangled state . AME(5,2) 1 ebit 2 ebit

  21. Deporalizing channel The depolarizing channel is a model of a decohering qubit with probability p the qubit remains intact, while with probability 1- p an “error” occurs. If an error occurs, then evolves to an ensemble of the three states all occurring with equal likelihood. (Bit flip + Phase Flip + Both)

  22. One parameter family q

  23. Cavity QED where ancilla is the cavity mode

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