would like to perform a measurement on his signals. He shall first inform Alice of his intention. Afterwards, one way to proceed is the following: They choose some convenient point, say the $m$-th signal, to stop and consider quantum Huffman coding for only the first $m$ signals and complete the encoding and decoding processes.

We shall consider two subcases. In the first subcase, the number $m$ is chosen such that the $m$-th signal is most likely still in the sender (Alice)’s hands. \[e.g. $m > K + O (\sqrt{K})$ in the asymptotic limit.\] The sender Alice now disentangles the remaining signal from the first $m$ quantum signals by applying a quantum shifting operation. She can now complete the encoding process for quantum Huffman coding of the $m$ signals and send Bob any un-transmitted qubits on the tape. In the asymptotic limit of large $K$, $O
(\sqrt{m})$ qubits of forward transmission (from Alice to Bob) are needed. (The required depth of the network is polynomial in $\log m$ if a parallel implementation of a quantum gate array is used.) In addition, Alice must send her record of the total length of the signals. However, this requires only an additional $\left\lceil \log
