here is my simplistic understanding

the photon has many possible properties, e.g polarisation, wavelength, position, arrival time etc.  some of these state spaces are finite in their dimensions (e.g. polarisation) which limits the information capacity of a photon encoded in this variable.  other state spaces are continuous (e.g. arrival time) and in principle the information that could be encoded in these spaces is unlimited.  however, continuous state spaces are effectively paired such that precision in one leads to uncertainty in the another.  taking our timing example a precisely measured arrival time implies a very broad range of frequency.  if the range of optical frequency is limited then this sets (through the uncertainty principle) the minimum size of time bin.  the duration of the experiment then sets an upper limit to the number of distinct time bins and hence the total information.   

another example might be using lateral position of the photon as an information carrier, the maximum number of states (and hence information content) being derived from the ratio of the field of view to the minimum resolvable distance supported by the optical system.

so i would argue that the maximum information that can be encoded on a photon is limited by the technological implementation under the constraint of the uncertainty relationships.

Many thanks Soren for your answer. So in this case we can "theoretically" encode infinite information on a single photon. But is there a theoretical upper bound on the energy that a photon can carry ? or maybe we can ask: how short can the wavelength of light be ?

Dear Akram Al-Hourani 

It depend upon the mass, and energy of information which need to be carried. frequency  and charges might do matter for its ranges due to structural and functional aspects.

Regards,

A single photon carries no information.

For obtaining or transmitting information, you need many photons. Alternatively, you need knowledge of the mode of preparation of that single photon.

If you know nothing a priori about how the photon was prepared, you get no information. For instance, a single photon can be part of a thermal beam. In a thermal beam there is a distribution of energy. Your photon can have the most probable energy in the distribution, or it may be from one tail of the distribution.

The same about the polarization. Passing a photon through a polarizer you get that the photon passed or not, but you can't know whether the photon was prepared with a fixed linear polarization, or circularly polarized, or simply with no defined polarization.

In teleportation experiments, you know a couple of things about the mode of preparation of the photon. Still, performing measurement on the photon you'd get no information, unless you receive classical bits of information about how to decodify the result of the photon measurement.

Spin up or spin down are the two states used in entanglement studies over optical net works. Wave length might be quantized to a certain number of Planck lengths, but we can't count them, and can only argue opinions about what continuum means.

The dual behavior of photons also matters, which depends on the experimental conditions involved; in some cases one may speak about one photon interaction.

Jerry,

Spin up, or spin down, means, for photons, right or left polatization. I hope that you mean up and down with respect to the propagation direction, otherwise you can't speak of photon spin.

Soren,

As you were so kind to downvote me, you should also explain what you find wrong in my answer. Any physicist who has knowledge in quantum mechanics would say that my answer is correct. A single photon contains no ninformation. One should use many photons, or, alternatively, additional information has to be passed between the sender and receiver.

Cowardice discreditates the respective person.

Best regards,

Sofia

here is my simplistic understanding

the photon has many possible properties, e.g polarisation, wavelength, position, arrival time etc.  some of these state spaces are finite in their dimensions (e.g. polarisation) which limits the information capacity of a photon encoded in this variable.  other state spaces are continuous (e.g. arrival time) and in principle the information that could be encoded in these spaces is unlimited.  however, continuous state spaces are effectively paired such that precision in one leads to uncertainty in the another.  taking our timing example a precisely measured arrival time implies a very broad range of frequency.  if the range of optical frequency is limited then this sets (through the uncertainty principle) the minimum size of time bin.  the duration of the experiment then sets an upper limit to the number of distinct time bins and hence the total information.   

another example might be using lateral position of the photon as an information carrier, the maximum number of states (and hence information content) being derived from the ratio of the field of view to the minimum resolvable distance supported by the optical system.

so i would argue that the maximum information that can be encoded on a photon is limited by the technological implementation under the constraint of the uncertainty relationships.

In the context of radiative decay of excitons, a single photon DOES carry some information. Suppose you begin with an initial state of a correlated electron-hole pair or exciton. It may undergo interactions with impurities,  defect assisted scattering,  trapping by surface  states, exciton-exciton  annihilation , capture by mid-gap defects or phonon assisted relaxations. And the exciton then undergoes  radiative decay during which it .  emits a single photon. Just one minute photon is enough to tell us that the exciton has collapsed. That is information. Very useful information to help fabricate optical devices .Never underestimate the power of one qubit, which in this case relates to the absence or presence of one photon. In agreement with @Padgett

As you define Information (= change of states of properties) I think we can't answer that question definitly. Out of Information Sciences all the usage of the word Information shows that there are properties which are not explainable in physically definitiv way.

Information is something which is interesting for Human Being. If we know exact we make a definitive scientific nomination for that "something new" . Then it is an explainable object.

We should say: a photon carries a lot of Data. Information in latest version needs Human reaction. My opinion is that we are in the phase of collecting data about photons. The object of interest for real Information is a photon really. We are not yet able to define certain states, we don't know how entanglement is effective, we don't know what is happening inside a photon. All that is Information - but not yet defined Data.   

See  also slide 5 of  

http://www.plbg.at/Werke/english/Foundations%20of%20HO.pdf

Dear Sofia,

=>A single photon carries no information

A photon can be defined in terms of its energy as well as its linear and angular momenta.  Each of these physical quantities can have infinite number of values. Therefore, a single photon can carry an infinite amount of information. 

Alternatively, corresponding to the emission of each photon, the Bloch vector of the atomic states 'changes' which has infinite possibilities. Therefore, each photon can be carrying the signature of the atomic state out of infitely possible states.

So again, a photon can carry an infinite amount of information.

Reading all answers I would like to say that Information of a photon is not definable exact.  That depends on ability to measure single properties.

I wouldn't dare to say Information of a photon (= summary of all properties) is infinit.