In super dense quantum coding, as described for example in Superdense coding, Bob changes the state of his photon, but it is still considered entangled with Alice's. I do not understand how this operation does not break entanglement. I would say that Bob's photon gets entangled with Bob's polarizer atoms and so on...
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"I entangled a classical bit into the system" is just a fancier way of saying "I encoded a message into the system".
If the message you were encoding into the system were composed of qubits, then you would have to worry about issues such as monogamy of entanglement. For example, see this quantum communication puzzle based on that fact. For communicating classical bits these issues are simply not a problem. Superdense coding changes which Bell basis state the system is in, but the system is still going to be in a Bell basis state and every Bell basis state is maximally entangled.
answered Jul 18, 2017 at 16:52
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$\begingroup$ THX! Anyway, regardless of classical or quantum bit discussion, I still cannot see how can I physically interact with one of the photons without breaking the entanglement with the other. Could you elaborate on this? Isn't decoherence a fancy way of saying "the system interacts with the environment"? Excuse me, but I must miss something fundamental... $\endgroup$ Commented Jul 19, 2017 at 8:12