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If is an element of reality then

If is an element of reality then. For dichotomic variables:. If then is an element of reality. Two useful theorems:. If is an element of reality then. For dichotomic variables:. If then is an element of reality. The three box paradox. Tunneling particle has (weak) negative kinetic energy.

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If is an element of reality then

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  1. Ifis an element of reality then

  2. For dichotomic variables: Ifthenis an element of reality

  3. Two useful theorems: Ifis an element of reality then For dichotomic variables: Ifthenis an element of reality The three box paradox Tunneling particle has (weak) negative kinetic energy

  4. Weak Measurement of The particle pre-selected The particle post-selected Weakmeasurements performed on a pre- and post-selected ensemble Pointer probability distribution !

  5. Robust weakmeasurement on a pre- and post-selected single system The system of 20 particles Pointer probability distribution Weak Measurement of 20 particles pre-selected 20 particles post-selected !

  6. Superposition of Gaussians shifted by small values yields the Gaussian shifted by the large value Properties of a quantum system during the time interval between two measurementsY. Aharonov and L. Vaidman PRA 41, 11 (1990) Another example: superposition of positive shifts yields negative shiftA. Botero

  7. Generalized two-state vector protection

  8. PRL 58, 1385 (1987) protection

  9. What is the past of a quantum particle?

  10. Wheeler: The “past” and the “Delayed Choice” Double-Slit Experiment J.A. Wheeler 1978 The present choice of observation influences what we say about the “past” of the photon; it is undefined and undefinable without the observation. No phenomenon is a phenomenon until it is an observed phenomenon. My lesson: The “past” of the photon is defined after the observation

  11. Wheeler delayed choice experiment Wheeler: The photon took the upper path It could not come the other way

  12. Wheeler delayed choice experiment Wheeler: The photon took both paths Otherwise, the interference cannot be explained

  13. Interaction-free measurement Did photon touched the bomb? Wheeler: The photon took the upper path It could not come the other way

  14. The past of a quantum particle can be learned by measuring the trace it left

  15. Wheeler delayed choice experiment Wheeler: The photon took the upper path It could not come the other way The trace shows Wheeler’s past of the photon

  16. Wheeler delayed choice experiment Wheeler: The photon took both paths Otherwise, the interference cannot be explained The trace shows Wheeler’s past of the photon

  17. Interaction-free measurement No No Yes Did photon touched the bomb? Operational meaning: Nondemolition measurements show NO!

  18. Wheeler delayed choice experiment Yes No No Yes Operational meaning: Nondemolition measurements show that the photon took the upper path

  19. Where is the photon when it is inside a Mach-Zehnder interferometer? Yes No Yes Operational meaning: Nondemolition measurements show that the photon took one of the paths But nondemolition (strong) measurements disturb the photon

  20. Where is the photon when it is inside a Mach-Zehnder interferometer? YesorNo or YesorNo Half a photon No or Half a photon Yes Operational meaning: Weak measurements (no disturbance at the limit) The information is obtained from weak measurements on an ensemble of identically prepared photons “Half a photon” or half the times the photon passes each path

  21. Wheeler delayed choice experiment Yes No No Yes Operational meaning: Weak measurements (no disturbance at the limit) The information is obtained from a pre- and post-selected ensemble

  22. Interaction-free measurement Yes No No Yes Did photon touched the bomb? Operational meaning: Weak measurements The information is obtained from a pre- and post-selected ensemble

  23. Interaction-free measurement No No Yes Did photon touched the bomb? Strong measurements Operational meaning:

  24. Interaction-free measurement No Yes Did photon touched the bomb? Operational meaning: Weak measurements (no disturbance at the limit) The information is obtained from a pre- and post-selected ensemble

  25. Wheeler delayed choice experiment No Yes Operational meaning: Weak measurements (no disturbance at the limit) The information is obtained from a pre- and post-selected ensemble

  26. Interaction-free measurement No Yes Did photon touched the bomb? Operational meaning: Weak measurements (no disturbance at the limit) The information is obtained from a pre- and post-selected ensemble

  27. The best measuring device for pre-and post-selected photon is the photon itself Strong measurements Yes

  28. The best measuring device for pre-and post-selected photon is the photon itself Strong measurements No

  29. The best measuring device for pre-and post-selected photon is the photon itself Weak measurements Yes

  30. The best measuring device for pre-and post-selected photon is the photon itself Weak measurements No

  31. Wheeler’s argument: “The photon took the upper path because it could not come the other way” seems to be sound. Its validity is tested in a best way by weak measurements using external system or the photon itself. The presence of the bomb can be found without anything passing near the bomb Can we find that the bomb or anything else is not present in a particular place without anything passing near this place? Yes! Hosten,…Kwiat, Nature439, 949 (2006)

  32. Kwiat’s proposal

  33. Kwiat’s proposal

  34. Kwiat’s proposal

  35. Kwiat’s proposal

  36. Kwiat’s proposal Wheeler: We know that the bomb is not there and the photon was not there since it could not come this way. Weak measurements: the photon was there!

  37. Kwiat’s proposal No Yes No Weak measurements: the photon was there! But it was not on the path which leads towards it!

  38. Kwiat’s proposal Weak measurements: the photon was there! But it was not on the path which leads towards it! Yes

  39. Kwiat’s proposal Weak measurements: the photon was there! But it was not on the path which leads towards it! No

  40. Kwiat’s proposal Weak measurements: the photon was there! But it was not on the path which leads towards it! No

  41. Kwiat’s proposal Weak measurements by environment

  42. Kwiat’s proposal Weak measurements by environment

  43. Kwiat’s proposal Weak measurements: the photon was there! But also in another place

  44. Kwiat’s proposal Weak measurements: the photon was there! But also in another place. The effects are equal! Yes

  45. Kwiat’s proposal Weak measurements: the photon was there! But also in another place. The effects are equal! Yes

  46. The two-state vector formalism expalnation The pre- and post-selected particle is described bythe two-state vector The outcomes of weakmeasurements are weak values

  47. The two-state vector formalism expalnation

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