# Information carried by single photon

In Quantum Information we can use photons for quantum bits (qubits). What i often read is that each photon can carry one unit of information, i.e. using the polarization state of a single photon.
I have two questions:
1) i read on this article that it is possible to send 1.63 bits of information per photon, what does that mean?
http://www.newscientist.com/article/dn13522-twisting-light-packs-more-information-into-one-photon.html#.Uy1cKBx22QE
2)If i can take a single photon state as a tensor product of its polarization state and its orbital angular momentum state (we could also add a frequency state), can i say that i am sending 2 (or 3) qubits of information in one single photon?
Thank you

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## 1 Answer

1) Basically, it seems what they implemented a version of the superdense coding theorem. What's that about? Well, the idea is the following:

As always, Alice wants to send bits to Bob. Before they start, however, they already establish a connection by sharing a maximally entangled state $|\Phi\rangle=\frac{|00\rangle+|11\rangle}{\sqrt{2}}$. So, in principle, they take a two-photon state and each of them has one photon. Alice can now act on her photon and produce (via local transformation) any of the four Bell states that are available. She can then send her photon to Bob and Bob can measure the two-photon state, obtaining one of the four Bell states (depending of what Alice did). So during the protocol, Alice sent ONE photon but Bob obtains TWO bits of information (four possible outcomes). So it seems that you can actually send two bits of information with one photon.

Now it seems that in the experiments, this is not really possible (you cannot measure every Bell state for example, but only three of them) and this is how the number 1.63 comes about. However, this does in no way contradict what you heard, because we didn't really send two bits of information with one photon. What we did is, we sent TWO photons - the first one before the real sending of a message started and the other one during the protocol (the entangled pair will be created by either Alice or Bob and one of these photons has to be sent to the other party).

2) Speaking about the bound, this also gives you an answer to the second question: There is actually nothing saying that a photon can only ever contain one bit of information. What the theorem says is that a qubit (i.e. a two-level quantum system) can only be used to send one classical bit - if we assume no prior entanglement (otherwise, we can use the protocol above). However, if your phyiscal system has more than two levels, you can use that to convey more information. The polarization states of a photon form a two-level quantum system, hence they can be used as a qubit. If, in your system, there are more degrees of freedom available, you can use them for additional storage of information.

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