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Quantum networks or quantum internet are terms that can be found when reading about quantum computation and information nowadys, but still I they are pretty vague concepts that are still in development.

I was wondering about the fact that this networks or internet would be pretty limited in communications between several computers as sending redundant information to several of them would be prohibited because of the no-cloning theorem. That would mean that only point-to-point communications could be done in quantum network. Moreover, once sent the information cannot be sent again as no copies of it are remaining, and so the communication could be done just once or the state should be created again by doing the same computations as before each time we want to send it. This sounds pretty inefficient coparing to the classical networks and internet.

Am I right about this thought or am I missing something?

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Setting aside the practical problems in actually building such things, quantum computers/networks can do everything their classical counterparts do without any fundamental overhead.

Your reasoning seems to stem from a misunderstanding of the no-cloning theorem. The no-cloning theorem says that you cannot reversibly clone unknown states with a protocol that does not depend on the state being cloned (see e.g. this question).

This has nothing to do with the communication context that you mention. If I want to send you some classical information, I would do it in basically the same way as it is done in a "classical" network. If I want to send you a quantum state, and I know what that state is, again there are no problems in "cloning" that state (I can just generate the same state many times).

If I have an unknown state and I want to send you many copies of it, then yes, the no-cloning theorem prevents me from doing so. However, it is not clear why should I want to do this for communication purposes.

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  • $\begingroup$ I see the point you give, but anyway this is not what I want to address with this question. For example, imagine that some computations are done in the computer and so the ending state is unknown, so now if we want to copy such state we cannot do it as it will be arbitrary and the broadcast won't be possible. This makes sense as the computations are done in order to obtain something that it is not known, as if it was known then doing the computations would be unnecessary. $\endgroup$
    – Josu Etxezarreta Martinez
    Jun 21, 2018 at 15:44
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    $\begingroup$ @JosuEtxezarretaMartinez but that doesn't really have much to do with communication. It is a known and important characteristic of QC that when the output of a computation is a quantum state, then one has to take into account the cost of reconstructing such state (if that is needed). But this is taken into account when talking of the costs of a given algorithm. In this sense, no-cloning prevents from reconstructing a state from a single copy of it, which is a known and well taken into account property of QC $\endgroup$
    – glS ♦
    Jun 21, 2018 at 15:53
  • $\begingroup$ If the cost of reconstructing the state is taken into account, then I reckon that the broadcasting can be done. However, I do not understand why you state that it does not have to do much with communications because if we want to share the output of some computation with some other computers, then such reconstruction should be done for the sake of sharing it with several receivers. I think about communications as where you do not always know exactly what are you transmitting to the receiver, so such things must be taken into account. $\endgroup$
    – Josu Etxezarreta Martinez
    Jun 22, 2018 at 7:55
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I have found this paper in which an insight about the question can be seen as the author states the difficulty of constructing the so-called quantum repeaters for quantum networks due to the no-cloning theorem. However, the constructions are indeed possible. The aforementioned paper is can be found here. The same author has a book called Quantum Networking where I consider that he will go further in explaining such difficulty and how to overcome it, but I do not have access to such text, so I am not sure if such explanation is given there.

I am giving this information as an answer so that other users interested in quantum networking can find information about the question that is being asked here.

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