Time Delay on Multiple Photons when travelling from one plac

[Cael]

I'm trying to understand the time delay induced on each photon when several individual photons travel in an open space from a sender to a receiver for example in the application of Quantum Key Distribution. So what I understand so far is light(photon) travel around 299,792 km (186,282 miles) per second. If I were to send 5 individual photons over to the other side from sender to receiver through an open space using a laser, let's say 50 km (31.0686 miles), it would take 0.167 ms to reach the receiver.

Therefore, I want to know if it is TRUE for every individual photon (that it will take 0.167 ms to reach receiver) or will there be slight variation on the time delay for every individual photon? With that said, can time delay be calculated that precisely when calculating the time taken for a photon to travel from one sender to another (receiver): Assuming time stamp are attached to each photon when sent and another time stamp are attached once received.

Feel free to correct me if my facts/calculations are wrong.

 

[mfb]

Technically photons don't have a well-defined position. In practice you'll see them traveling at the speed of light within the time resolution of the source and the detectors (which depends on the setup).

 

[Cael]

Technically photons don't have a well-defined position. In practice you'll see them traveling at the speed of light within the time resolution of the source and the detectors (which depends on the setup).

True but one can still measure the time taken to reach the receiver, right? I'm just not sure if every photon have the same time taken to travel from sender to receiver or additional delay will be induced due to certain circumstances.

 

[Cael]

I have another idea. What if photons are transmitted through fibre optics? Photon may travel slower in fibre optics but the time taken for each photon to travel to the other side should be constant, right?

 

[DrChinese]

I have another idea. What if photons are transmitted through fibre optics? Photon may travel slower in fibre optics but the time taken for each photon to travel to the other side should be constant, right?

As mfb said: You will always measure c (for that medium) within the resolution of detection. You don't see any variation to speak of.

 

[f95toli]

Just to add to what was said above.

When asking questions like this it is important to distinguish between an "ideal" experiment and the real world.
In an ideal experiment you would (obviously) not detect any difference between different photons because nothing would change between sending the first and second photon. However, in real experiment it is possible (or if you are sending photons long distances even likely) that you WILL see a difference; especially if the signal is sent in a fibre or -even worse- open air.
The reason is that photons sent at different times can (and probably will) end up travel different effective distances; "effective" here means that some property that affects the speed of light in the medium has changed. The typical example would be vibrations that cause the path length in a fibre to change somewhat. In open air it could be something as simple as turbulence locally changing the density of air (the same effect that can make stars blurry when seen from the ground)

Note that the timing jitter for a good single photon detector is around 15 ps. Hence, 157 us is a VERY long time meaning even very small changes can be easily detected.

Sending photons with low jitter over long distances is these days a fairly specialized area of science and has many applications; not only on QKD but also in e.g. clock distribution etc.