Quantum bomb detection: Tasks Part 2 for students

Quantum bomb detection Worksheet Part 2

Part 2: A measurement destroys the superposition

Open the website with the Quantum Flytrap game 'Peeking at a photon'. This game was created by Piotr Migdał and designed by Klem Jankiewicz.
The goal of the game is to change the setup of a Mach-Zehnder interferometer such that 50% of the photons reach detector 1 and 50% of the photons reach detector 2.

Screenshot flytrap quantum game alpha — © Screenshot
Screenshot Game 'Peeking at a photon'

Task: Get familiar with the setup and modify it

Emit photons by clicking on the laser. The photon is going into a superposition state, $\frac{1}{\sqrt{2}} | d o w n ⟩ + \frac{1}{\sqrt{2}} | r i g h t ⟩$ , after it has passed the first beam splitter. After the second beam splitter, the photon is detected by the detector at the right only – due to interference. So, the photon ends up in the state |right⟩ in all cases.
Find out what you have to change in order for the photon to be detected in both detectors with a 50% probability. Little hint: there is one element that you can move around.

Have you succeeded?

Reload the webpage and insert the moveable detector in one of the paths, let’s say the right path of the photon.
Observe the behaviour of the photon as it goes through the interferometer.
By inserting the movable detector in the right path, you perform a measurement – you check whether the photon took the right path or not. This changes the behaviour of the photon and the superposition state. After the measurement, the photon is either in the right path (it was detected by the movable detector) or in the lower path (it was not detected by the movable detector).

Summary & Conclusion Summary & Conclusion

The following table resumes what happens:

	Photon
Initial state	$\| i n i t i a l ⟩$
After beam splitter 1	superposition state: $\frac{1}{\sqrt{2}} \| d o w n ⟩ + \frac{1}{\sqrt{2}} \| r i g h t ⟩$
After the measurement	either $\| d o w n ⟩$ or $\| r i g h t ⟩$
After beam splitter 2	superposition state: $\frac{1}{\sqrt{2}} \| d o w n ⟩ + \frac{1}{\sqrt{2}} \| r i g h t ⟩$
Detection	50% of the classical particles are detected by detector 1. 50% of the classical particles are detected by detector 2

Conclusion:

A measurement changes the state of the photon. In the experiment above, it destroys the superposition state $\frac{1}{\sqrt{2}} | d o w n ⟩ + \frac{1}{\sqrt{2}} | r i g h t ⟩$ . After the measurement, the photon is in either state $| d o w n ⟩$ or $| r i g h t ⟩$ .