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Entanglement and its Applications

Entanglement and its Applications. By Nasser Metwally Math. Dept., Faculty of Science, Aswan University 25/7/2012. Entanglement and its Applications. The Paradox of Enstein, Podolsky and Rosen (EPR) Systems Correlations Entanglement Applications. Example.

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Entanglement and its Applications

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  1. Entanglement and its Applications By Nasser Metwally Math. Dept., Faculty of Science, Aswan University 25/7/2012 N. Metwally, Math. Dept. College of Science Bahrain University

  2. Entanglement and its Applications The Paradox of Enstein,Podolsky and Rosen (EPR) Systems Correlations Entanglement Applications. Example N. Metwally, Math. Dept. College of Science Bahrain University N. Metwally, Math. Dept. Faculty of Science, Aswan University

  3. The Paradox • Two particles are interact inpast. • The two particles are remote from each other. May be!! See you later N. Metwally, Math. Dept. College of Science Bahrain University N. Metwally, Math. Dept. Faculty of Science, Aswan University

  4. The Paradox • Measurements on one particle do not affect on the other particle. This result inconsists with the quantum mechanics. Einsteinand Podolsky and Rosen climed that quantum mechanics is incomplete. N. Metwally, Math. Dept. College of Science Bahrain University N. Metwally, Math. Dept. Faculty of Science, Aswan University

  5. The Paradox Entanglement is one of the properties ofquantum mechanics which causedEinsteinand others to dislike the theory . Einsteincalled it a non-Locality property This is reallyso bafflingand surprising N. Metwally, Math. Dept. Faculty of Science, Aswan University

  6. The Paradox Enstein: quantum state of the system does notcompletelly describe this phenomena , Enstein:there are additional “ hidden “variables that are missing in the quantumstate, Schrodingercoined the termentanglementfor this aspect of quantum nechanics N. Metwally, Math. Dept. College of Science Bahrain University N. Metwally, Math. Dept. Faculty of Science, Aswan University

  7. What is theentanglement? Quantum System Classical Correlated Quantum Correlated Entangled Separable N. Metwally, Math. Dept. College of Science Bahrain University N. Metwally, Math. Dept. Faculty of Science, Aswan University

  8. Physically • *A state is calledseparableif It can be • prepared by two parties Alice and Bob in • a classical way. • A density opertator that created in this way • contains only aclassicalcorrelations. N. Metwally, Math. Dept. College of Science Bahrain University N. Metwally, Math. Dept. Faculty of Science, Aswan University

  9. Mathematically • A state  is separable iff • Where • see Werner PRA404277 (1989) • Finding such a decompoistion is anon-trivial task N. Metwally, Math. Dept. College of Science Bahrain University N. Metwally, Math. Dept. Faculty of Science, Aswan University

  10. How do you know a given stateis separable or not? Peres-Horodecki criterion: Astate is separable if all the eigenvaluesof itspartial transposeare non-negative This criterion is a necessary andsufficient for systems of 2 x 2 Or 2 x 3. It is only necessary for large systems. Peres, PRL 77,1413 (1996). M.,P.,R., Horodecki, Phys.LettA 222,1,1996 N. Metwally, Math. Dept. College of Science Bahrain University N. Metwally, Math. Dept. Faculty of Science, Aswan University

  11. The set of all states All states NPT undistillable PPT Entangled PPT Separable N. Metwally, Math. Dept. College of Science Bahrain University N. Metwally, Math. Dept. Faculty of Science, Aswan University

  12. Entanglement Measures Ent. of Distillation. Ent. of Formation Mixed State Pure states More to come !! Distance Negativity Von Neummen Entropy. Concurrence N. Metwally, Math. Dept. College of Science Bahrain University N. Metwally, Math. Dept. Faculty of Science, Aswan University

  13. Entanglement Applications Teleportation Entanglement Q. Computing Cryptography Data Processing N. Metwally, Math. Dept. College of Science Bahrain University N. Metwally, Math. Dept. Faculty of Science, Aswan University

  14. N. Metwally Submit to physics. Scripta (2007) PPT CriterionFor Two Particles Pass In Bloch channel Bloch Channel Bloch Channel Lab. For Ent. Pairs N. Metwally, Math. Dept. Faculty of Science, Aswan University

  15. N. Metwally Submit to physics. Scripta (2007) Degree of Entanglement Negativity N. Metwally, Math. Dept. Faculty of Science, Aswan University

  16. N. Metwally Submit to physics. Scripta (2007) Eberly and Abdel-Aty Sudden Death Of Entanglement N. Metwally, Math. Dept. Faculty of Science, Aswan University

  17. Quantum Communication Do you have it? I have it, but how can I send it!! Do not Worry !!!, We have A method N. Metwally, Math. Dept. Faculty of Science, Aswan University

  18. State Communication Protocol By Metwally State Test. U. Op+M. I gain all the Inf.. I lost My Inf. N. Metwally, Math. Dept. Faculty of Science, Aswan University

  19. Thank you N. Metwally, Math. Dept. Faculty of Science, Aswan

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