The two-state vector. ? ? At time t: ? Erasing the past.

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Presentation transcript:

The two-state vector

?

? At time t:

?

Erasing the past

Alternative past for the same present Hint:

protection Erasing the past protection

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

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

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

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

? ? ?? ? ?

A single pre- and post-selected system ?

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

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

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

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?

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

The Aharonov-Bergmann-Lebowitz (ABL) formula:

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

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

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: ?

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!

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

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

The three box paradox It is always in !

The three box paradox It is always in

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

איך לסגור N חורים עם פקק אחד

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

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

A B C

A B C 0

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