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When you enter the field of quantum communications, you run at some point into the concept of superdense coding.

Basically it is a way to encode classical bits on the qubits of a quantum channel, which sounds interesting in the first place to increase classical throughput by benefitting of the exponential growth of the Hilbert space with multiple qubits.

Yet when you look at the protocol in more detail, you understand that even though it seems that you have encoded 2 classical bits in 1 qubit, you actually need a second, entangled, qubit to retrieve the information from the 1st qubit.

So there is no real benefit - if you need to send two photons, you can encode two bits classically.

So apart from a textbook example, where is the practical interest? Are there more subtle points I am missing? Are there more intricatre protocols to avoid that?

Cross-posted on math.SE

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No, you need to send only one photon (from the pair). The other party could generate entangled pair and send the entangled photon to you. Or it could be the third party that send both of you your photons $-$ prior to actual communication.
Even if it's you who generate the entangled pair and share the entangled photon $-$ you could do it way before the time when you need to send the second photon that carry the actual information.

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  • $\begingroup$ But you still need to send two qubits as in case of classical serial communication. $\endgroup$
    – Martin Vesely
    Commented Jan 4, 2020 at 13:00
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    $\begingroup$ Technically, yes. But one of the qubits could be sent in the other direction way before the actual communication. $\endgroup$
    – Danylo Y
    Commented Jan 4, 2020 at 13:01
  • $\begingroup$ I see, thanks for explanation. $\endgroup$
    – Martin Vesely
    Commented Jan 4, 2020 at 13:10
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You could use superdense coding to partially time shift bandwidth, smoothing out network utilization. Or you could increase the bandwidth of a low latency link by sharing entanglement over a high latency link. https://algassert.com/quantum/2014/05/03/Storing-Bandwidth-with-Superdense-Coding.html

You can also use it to turn a two way link into a faster one way link. https://algassert.com/quantum/2015/01/17/Superdense-Coding-on-the-Fly-and-in-Reverse.html

All that being said, all of this assumes that sending a qubit is no harder than sending a bit, which seems very unlikely to me. Bits effectively are immune to more noise which makes their bandwidth much higher.

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I think that sending in advance entangled qubits does not solve the issue: actually, the problem is produced by the fact that in telecommunication systems it would be necessary to share (and store) in advance an “infinite” number of entangled qubits! Which is practically without sense.

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