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

2. Information is physical Info Phys

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

5. 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 QInf

6. No Clon 1

7. No Clon 2

8. State discrimination    1 ≠0 no way to discriminate with certainty error probability P e = z 0 P 10 + z 1 P 01 P ij = Tr [  j  i ] Optimal detection  1 =  >0 | >< |  0 =  -  1  | >= | >  = z 1  1 - z 0   Minimum error (pure states) open problems: - mixed states - asymm. sets - … St Discr

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

25. Toffoli