1. The two-state vector

2. ?

3. ? At time t:

4. ?

7. Erasing the past

8. Alternative past for the same present Hint:

9. protection Erasing the past protection

11. A=? Are there any differences between what can be done to and ? Nondemolition (von Neumann) measurements ?

12. U U Unitary transformation Are there any differences between what can be done to and ? ?

13. The two-state vector is a complete description of a system at time t ? The two-state vector is what we can say now ( ) about the pre- and post-selected system at time t The two-state vector describes a single pre- and post-selected system, but to test predictions of the two-state vector we need a pre- and post-selected ensemble

14. ? ? ?? ? ? The pre- and post-selected ensemble

15. ? ? ?? ? ?

16. A single pre- and post-selected system ?

17. ? The two-state vector in the framework of the many-worlds interpretation of quantum mechanics

18. A single pre- and post-selected system ? The two-state vector in the framework of the many-worlds interpretation of quantum mechanics The other world

19. A single pre- and post-selected system ? The two-state vector in the framework of the many-worlds interpretation of quantum mechanics This world

21. The two-state vector is a complete description of a system at time t ? The two-state vector is what we can say now ( ) about the pre- and post-selected system at time t So, what can we say?

22. The Aharonov-Bergmann-Lebowitz (ABL) formula: described by the two-state vector: Measurements performed on a pre- and post-selected system

23. The Aharonov-Bergmann-Lebowitz (ABL) formula:

24. Measurements performed on a pre- and post-selected system described by the two-state vector: The Aharonov-Bergmann-Lebowitz (ABL) formula:

25. Measurements performed on a pre- and post-selected system described by the two-state vector: The Aharonov-Bergmann-Lebowitz (ABL) formula: At time t:

26. Measurements performed on a pre- and post-selected system described by the two-state vector: The Aharonov-Bergmann-Lebowitz (ABL) formula: Can we arrange at time t: ?

27. 3 CUPS GAME NEW RULES You win when you do not find the ball You can look only under one of the two cups The dealer does not see your action, but he can look at the ball later and cancel a particular run of the game Quantum dealer can win without cheating!

28. The ball is a pre- and post-selected system ? The two-state vector

29. Where is the ball? ? Aharonov and Vaidman, JPA 24, 2315 (1991) Aharon and Vaidman, PRA 77, 052310 (2008) The 3-boxes paradox Vaidman, Found. Phys. 29, 865 (1999)

30. The three box paradox It is always in !

31. The three box paradox It is always in

33. A single photon “sees” two balls It scatters exactly as if there were two balls Y. Aharonov and L. Vaidman Phys. Rev. A 67, 042107 (2003)

34. איך לסגור N חורים עם פקק אחד

36. 0 The outcome is 0. The computer was not running! Simple Counterfactual Computation with Outcome 0. Kwiat has to be right!

37. 0 The computer was running! Kwiat cannot be right! A B C Kwiat’s scheme = 3-boxes paradox

38. A B C

39. A B C 0

40. 0 A B C Kwiat cannot be right! There is no difference between A and B: counterfactually it is in A as it is in B the same quantum descriptions in A and in B Kwiat’s scheme = 3-boxes paradox