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Elitzur-Vaidman tester

Puzzle:

or

The box has two holes on opposite sides (photon can pass through)

However, the bomb is “photon-sensitive”: it explodes as soon as it is hit by a photon!

?

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Elitzur-Vaidman tester

Puzzle:

or

?

The box has two holes on opposite sides (photon can pass through)

However, the bomb is “photon-sensitive”: it explodes as soon as it is hit by a photon!

3 of 27

Elitzur-Vaidman tester

Puzzle:

?

The box has two holes on opposite sides (photon can pass through)

However, the bomb is “photon-sensitive”: it explodes as soon as it is hit by a photon!

Can you determine whether a bomb is present without making it explode?

Classically impossible!

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A quantum solution

mirror: reflects any photon that hits it

beam splitter: either lets a photon through�or reflects it, with probability 1/2 each

source: emits photons

detector: records any photon that hits it

mirror

beam splitter

A

detector

B

?

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A quantum solution

mirror

beam splitter

A

detector

B

Case 1: Box is empty

Our “classical” intuition:

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A quantum solution

mirror

beam splitter

A

detector

B

Case 1: Box is empty

Our “classical” intuition:

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A quantum solution

mirror

beam splitter

A

detector

B

Case 1: Box is empty

Our “classical” intuition:

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A quantum solution

mirror

beam splitter

A

detector

B

Case 1: Box is empty

Our “classical” intuition:

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A quantum solution

mirror

beam splitter

A

detector

B

Case 1: Box is empty

Our “classical” intuition:

10 of 27

A quantum solution

mirror

beam splitter

A

detector

B

Case 1: Box is empty

Our “classical” intuition:

photon lands at detector A, with 1/2 probability
photon lands at detector B, with 1/2 probability

..this intuition is false!

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A quantum solution

mirror

beam splitter

A

detector

B

Case 1: Box is empty

Turns out the photon is in a quantum state

and the beam splitter is a quantum gate!

It’s not that the beam splitter is “reflecting with prob. 1/2 and letting through with prob. 1/2”.

Rather the beam splitter is mapping the incoming photon to an �“equal superposition” of the two!

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beam splitter

A

detector

B

Case 1: Box is empty

What actually happens:

Photon always hits detector A!

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A quantum solution

mirror

beam splitter

A

detector

B

Case 1: Box is empty

H

detectors

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H

detectors

H

Let’s calculate what this circuit does:

H

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H

detectors

H

Let’s calculate what this circuit does:

H

Constructive interference

destructive interference

=

A quantum solution

mirror

beam splitter

A

detector

B

Case 2: Box contains a bomb

The bomb acts as a measurement!

With prob. 1/2 bomb explodes
With prob. 1/4 photon is detected at A
With prob. 1/4 photon is detected at B

In the last case, we know for sure that a bomb is present, but it did not explode!

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H

detectors

When bomb does not explode

”A” with prob. 1/2

”B” with prob. 1/2