חוק המכפלה

It is always in ! The 3-boxes paradox

Peculiar example: a failure of the product rule

פרדוקס של חרדי

Weak Measurements

Quantum measurement of

Weak quantum measurement of

The outcomes of weak measurements are weak values Weak value of a variable C of a pre- and post-selected system described at time t by the two-state vector

Weak measurement of with post-selection

The outcomes of weak measurements are weak values Weak value of a variable C of a pre- and post-selected system described at time t by the two-state vector

Weak value of a variable C of a pre- and post-selected system described at time t by the two-state vector The outcomes of weak measurements are weak values

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

How the result of a measurement of a component of the spin of a spin-1/2 particle can turn out to be 100 Y. Aharonov, D. Albert, and L. Vaidman PRL 60, 1351 (1988) Realization of a measurement of a ``weak value'' Realization of a measurement of a ``weak value'' N. W. M. Ritchie, J. G. Story, and R. G. Hulet Phys. Rev. Lett. 66, (1991) The outcomes of weak measurements are weak values

Observation of the Spin Hall Effect of Light via Weak Measurements Science 8 February 2008: Amplifying a Tiny Optical Effect K. J. Resch O. Hosten and P. Kwiat “In the first work on weak measurement (AAV), it was speculated that the technique could be useful in amplifying and measuring small effects. Now, 20 years later, this potential has finally been realized.”

Weak-measurement elements of reality If we can infer that the quantum wave of the pointer of the measuring device which measures C will, in the limit of weak interaction, be shifted without distortion by the value c, then there is a weak element o reality

Weak-measurement elements of reality If we can infer that the quantum wave of the pointer of the measuring device which measures C will, in the limit of weak interaction, be shifted without distortion by the value c, then there is a weak element o reality

Weak-measurement elements of reality If we can infer that the quantum wave of the pointer of the measuring device which measures C will, in the limit of weak interaction, be shifted without distortion by the value c, then there is a weak element o reality

Weak-measurement elements of reality If we can infer that the quantum wave of the pointer of the measuring device which measures C will, in the limit of weak interaction, be shifted without distortion by the value c, then there is a weak element o reality

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