The information capacity of a single photon (2012) | Hacker News Reader

The information capacity of a single photon (2012)

arxiv.org

62 pointsadamnemecek32 comments

Tl;dr by using the photon's color (wavelength), we get more bandwidth than the current qubit encoding, which is based on polarization.

This would be loosely similar to using multiple voltage levels to build trinary, quaternary, etc. digital circuits or CPUs. (Which has been done in the past and some people still speculate will come back into fashion.)

It's also somewhat similar to the idea of FM radio, where the signal is encoded in the frequency differences.

It looks like they dropped the polarization encoding to use wavelength only. If I'm reading it right, then I'd guess there an extra easy +1 bit (at least) by using both wavelength and polarization.

The answer from the paper:

Theoretically infinite, but in their more realistic model they came up with 5 bits.

The gap between 5 and infinite bits seems a bit on the large side.

In the abstract they claim it's because a photon state is in continuous space-time. But this isn't the same as the theoretical limits of detecting a state off a single photon, as instrumentation always destroys info.

Also, how sure are we that space-time is continuous?

We are, in fact, fairly sure it isn't: https://en.wikipedia.org/wiki/Planck_constant

AFAIK Planck stuff has no bearing on the discreteness of space itself.

You might be thinking of the Planck Length.

That and the Planck Time, yes.

In theory there is no difference between theory and practice but in practice there is.

If you calculate the gap for 4 to infinity and 6 to infinity, you can interpolate a pretty good approximation.

It is 32 States to infinity

and hence the question shall be 16 to and 64 to.

Reminds me of the problem that uses Graham's number, where the lower bound shifted from 6 to 11 to 13, and the upper bound is a number that exceeds the bounds of up arrow notation.

Graham's number is a reminder to me to be glad that my lifespan is finite.

A bit off topic, but the (not very good) novel The World at the End of Time inspired the same thoughts in me.

One of the narrators is an immortal being who can manipulate energy. He has a grand old time in his youth swimming around in the cores of main sequence stars, playing and thinking and scheming for billions of years. He manages to kill off all of his kin, ensuring his survival forever. But eventually the really desirable, hot stars start to burn out. He has to move to longer-living dwarf stars, and turn down his mental processes because they can't be completely supported with the reduced amount of energy available. The universe continues to age and the stars dim and he's forced to let go of large parts of his memory because he can't afford the energy expenditure to keep it coherent. He begins to fear for his continued survival, always hungry and searching for sources of energy. Much later, the stars have burned out to cinders and are nearly at thermal equilibrium with the - by now - extremely dim background radiation. He's terrified of black holes but their Hawking radiation is the best remaining source of energy in the universe so he gets close to a big black hole, a shadow of his former self, holding onto only a few core memories with the energy of the particles emanating from the event horizon. He hibernates for eons at a time, slowly gathering energy until he can afford a few moments of consciousness. The black holes of course eventually evaporate and he becomes effectively insensate, living off the meager energy of protons occasionally decaying.

Yeah, I don't want to live forever either.

I feel like that's a bit like saying what's the maximum speed of travel over land, in 1850 you might say "theoretically infinite or the speed of light, but practically, about the speed of a horse." The practical estimate is sort of useless because in a few decades there will be cars, jets, etc.

I mean, car/jet might as well be a horse compared to c.

The Juno probe hit 90,000 mph on a gravitational slingshot around Earth. That's about 0.00013 c.

Energy wise you need ~240,000,000x the energy to hit 0.5 C, so still a very long way.

Also, g forces are real problem for over land travel. In space you can eventually almost hit C by aiming for a black hole. But to stay on land you start hitting negative g's due to curvature and or high g forces to start and stop.

Parker space probe should set a new record at 430,000 mph on its closest approach around the sun!

Though when you're dealing with logarithms, a jet's only about twice as good as a horse.

May I ask whats the capacity of an electron?

Arbitrarily tunable orbital angular momentum of photons (2016) https://www.nature.com/articles/srep29212

If the holographic principle is true there are a lot less degrees of freedom than would otherwise seem available

The cardinality of a continuous 3d space is the same as a continuous 2d space. You just have to be clever about encoding it.

You have to hit black-hole-level information densities for it to matter, don't you?

yes, but that entails an upper-bound... finite.

When it comes to a single particle, I wouldn't have thought an infinite number of degrees of freedom "seem available" in the first place.

That is exactly what the article posits as a hypothesis.

Maybe? I would have said they're using one degree of freedom, the frequency.

As far as our model is concerned it's a distiction without a difference because were talking about all the bits of entropy, i.e. the information. If it's a represtanble state, it counts as a bit of information.

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