the encoder head will destroy quantum coherence. This decoherence effect is physically the same as a “which path” measurement that destroys the interference pattern in a double-slit experiment. One can also understand this effect simply by considering an example of $N$ copies of a state $a | 0 \rangle + b | 1 \rangle$. It is easy to show that if the encoder couples an encoder head to the system and keeps a record of the total number of zeroes, the state of each signal will become impure. Consequently, the fidelity between the input and the output is rather poor.

Storage of Quantum Signals
==========================

Nevertheless, we will show here that Huffman-coding inspired quantum schemes do exist for both storage and communication of quantum information. In this section we consider the problem of storage. Notice that the above difficulties are due to the requirement of instantaneousness. This leads in a natural way to the question of [*storage*]{} of quantum information, where there is no need for instantaneous decoding in the first place. In this case, the decoding does not start until the whole encoding process is done. This immediately gets rid of the second (namely, when to decode) and third 