How does a quantum repeater work without violating the no cloning theorem? Quantum repeaters work similar to classical repeaters to allow a qubit to be successfully communicated a longer distance before it is overwhelmed by noise.  There is significant  discussion of this on the WWW and in the published literature.  Recently, actual working models have been claimed on arXiv: here is one example: https://arxiv.org/abs/1811.10723.
How do these quantum repeaters avoid  violating  the no cloning theorem?  Can they be linked to provide essentially unlimited distance transmission of a qubit?  (analogous to a classical repeater with a classical bit?)
(This post has been  re-edited to be more comprehensible at the request of the moderators. If it is still unclear, I will need help in clarifying it further.)
 A: In quantum mechanics, a measurement will not disturb the system if the system is already in an eigenstate of the obserable being measured.
The "No cloning" theorem is the assertion that there is no physical process $U$ that can achieve
$$
U \left(| \psi \rangle | 0 \rangle \right) = | \psi \rangle | \psi \rangle
\;\;\;\;\; \forall \; | \psi \rangle
$$
but note the crucial FOR ALL part. It means you can't have a process which takes as input an unknown state, and gives as output two copies of that state, no matter what state it was.
A quantum repeater is doing a different job. It is a device used to set up one specific, known, entangled state between two places $A$, $B$. Once this is done then the situation can be used to pass a general unknown state $\psi$ from one place to another. The word 'repeater' here is only loosely comparable to its use in classical communication channels, but it is reasonably fair; it alludes to the part of the process where the entangled state is set up. This is done using methods such as entanglement swapping. If you have an intermediate place $C$ in between $A$ and $B$, then an entanglement between $A$ and $C$ can be combined with one between $C$ and $B$ to produce the one you want between $A$ and $B$. But note, this does not involve copying some general state, it involves producing one specific state.
After that the channel can be put into action, and the evolution is
$$
R \left( |\psi, \;A \rangle | |0, \;B \rangle |\right) = |0, \;A \rangle| \psi,\; B \rangle 
$$
where $\psi$ refers to a quantum state such as the state of a qubit, and $A$, $B$ refer to different physical locations, such as different cities on Earth. As you see, no copying is involved. 
