[stracer]

Is there some fundamental limit to the number of bits per photon that can be communicated via EM radiation? I think it does not exist, because photons aren't all equal, we can use very high frequency and X-ray quantum can probably carry much more information than RF quantum.

[resters]

this is called the Shannon limit. To discern signal from noise, a minimum sample rate of 2x the frequency of the signal is required. A signal is something that can be turned on or off to send a bit.

Higher frequencies can carry more data as you infer but the engineering challenges of designing transmitters and receivers create tradeoffs in practical systems.

[ganzuul]

In addition to wavelength EM also has several polarization modes and near/far field characteristics that can carry information.

[resters]

Can individual photons be measured for polarization and phase or is there a similar limit that requires more than one photon to do so? I suppose both are relative to some previous polarization or phase?

[stracer]

Polarization can be measured using polarization filter and light detector, but it is destructive in the usual sense of quantum theory. That is, if the detector after polarization filter clicks, we know the EM field had non-zero component in the direction of the filter, but we do not find out the other components it had before entering the filter.

[yyyfb]

I guess not without a minimum bound on the communication speed.

If you have a way to reliably transmit N bits in time T using P photons, you can transmit N+1 bits in time 2 * T using also P photons. What you would do to transmit X0,X1,...Xn is:

- During the first time slot of duration T, transmit X1,... Xn if X0 = 0 and 0 otherwise (assuming absence of photons is one of the symbols, which we can label 0)

- During the second time slot of duration T, transmit 0 if X0=0 and X1,... Xn otherwise

This only uses P photons to transmit one more bit, but it takes twice as long. So if you're allowed to take all the time that you want to transmit, and have really good clocks, I guess that theoretically this is unbounded.

[im3w1l]

Send three photons A B C. They arrive at times ta, tb, tc. Compute fraction (tc - tb) / (tb - ta). This can encode any positive real number with arbitrary precision. But clearly you need either very precise measurements or send the photons at a very slow rate.

[acchow]

Special relativity will give limits on how aligned the clocks can be (which should be a function of the distance between the clocks). So there will be precision limits.

[LegionMammal978]

Unless the clocks are accelerating, that shouldn't change the ratio between the two time differences, right? If the two ends have a constant velocity relative to each other, then each should perceive the other as being off by a fixed rate.

[ganzuul]

Good induction to thinking about quantum gravity.