In quantum information theory, classical-quantum channels are considered to be channels whose input is the realizations $x\in\mathcal{X}$ of a classical random variable to a quantum state $\rho_x^B$, that is


where each quantum state $\rho_x$ is described by a positive semi-definite operator with unit trace. This kind of channels are useful due to the fact that they arise in the reality, such as an optic fiber communication link, and so codes taking into account the impact of quantum mechanics can be constructed to make the link perform better.

I was wondering if someone can give reference about more examples of real life communication scenarios where this kind of channels can be useful to describe them apart from the optical link example that is the most typical one.

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    $\begingroup$ isn't any instance of controlled state preparation an example of such a channel? Virtually any experimental work of quantum information does it in some form or the other. $\endgroup$
    – glS
    Jan 22 '19 at 17:24
  • $\begingroup$ Such are good examples for the application of the cq-channel. However, I am looking for examples that may not seem straightforward for applying quantum mechanical points of view. For example, applying cq models to optical fiber communications was not straightforward for me to see, as classical coding schemes are very common to be used in such kind of links. Applying cq codes does anyway improve the performance of those due to the underlying quantum mechanical nature of those, so I am looking to find out more examples as such. $\endgroup$ Jan 23 '19 at 11:43
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    $\begingroup$ ah, I missed the "real-life" part of the question. Still, how much "real-life" do you want it to be? There are not that many examples of practical applications of QM at this stage, and all the ones I can think of are in the realm of quantum communication, and they all use light for long-range communication, so pretty much the case you already know about. Maybe examples of quantum communication via satellite link would qualify, as they don't use (only) fiber optics? $\endgroup$
    – glS
    Jan 23 '19 at 11:54
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    $\begingroup$ I mean communication of quantum information between ground and satellites, see e.g. this or this articles about it. Though the question then becomes essentially: what other ways are there to communicate classical information other then using fiber optics?. I don't think the link with the formalism of classical-quantum channels is very meaningful in this case $\endgroup$
    – glS
    Jan 23 '19 at 12:40
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    $\begingroup$ Yes for long-range communication light (and thus typically, but not necessarily, photons) is pretty much the only option (as of now at least). The information can be encoded in different degrees of freedom of the photon (polarization, position, frequency, orbital angular momentum, time), each one of which comes with its pro and cons. This I believe would make for a nice separate question (though it might be possible that something along this line has already been asked and answered either here or on physics.SE, so I would check that first). $\endgroup$
    – glS
    Jan 23 '19 at 12:42

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