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Matteo G A Paris Quantum Optics & Information Group Universit à di Milano qinf.fisica.unimi.it/~paris. Title. Informatica Quantistica: Introduzione. Milano, 30 Maggio 2005. Info Phys. Information is physical. Information is physical.

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  1. Matteo G A Paris Quantum Optics & Information Group Università di Milano qinf.fisica.unimi.it/~paris Title Informatica Quantistica: Introduzione Milano, 30 Maggio 2005

  2. Info Phys Information is physical

  3. Information is physical Coding: logical bit / physical degree of freedom (superpositions and non-orthogonality) Transmission, manipulation: Logical gates should be unitary. After interactions information carriers cannot be separately described (superpositions  entanglement) Decoding: uncertainty relations and impossibility of joint measurements

  4. Noise Reso Information is physical: quantum mechanics Superpositions (coherence) Entanglement Uncertainty relations Fluctuations Noise Resource

  5. QInf Quantum Information Impossible machines  cloning  quantum repeaters  limits to amplification  nonorthogonality  signal discrimination  joint measurements Quantum resources  parallelism  quantum computing  entanglement  teleportation  dense coding Quantum cryptography

  6. No Clon 1

  7. No Clon 2

  8. St Discr State discrimination  1≠0 no way to discriminate with certainty error probability Pe = z0 P10 + z1 P01 Pij = Tr [j i] Optimal detection 1= >0 |>< | 0=  - 1 |  >=  |  > = z1 1 - z0  • open problems: • mixed states • asymm. sets • … Minimum error (pure states)

  9. Joint M

  10. Crypto

  11. Q Crypto 1

  12. Q Crypto 2

  13. D cod 1

  14. D cod 2

  15. TLP

  16. Q Calc

  17. CTRL F

  18. Deutsch

  19. Grover

  20. Shor

  21. UnivGate1

  22. UnivGate2

  23. QC risorse

  24. Outro Open problems (among many others)  Implementations QC (scalable, robust against decoherence)  Quantum algorithms  Reversible computation  Characterization of entanglement

  25. Toffoli

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