sender and the receiver are forbidden to measure the length of each signal. We emphasize that this difficulty—that the sender is ignorant of the length of the signals to be sent—is, in fact, very general. It appears in any distributed scheme of quantum computation. It is also highly analogous to the synchronization problem in the execution of subroutines in a quantum computer: A quantum computer program runs various computational paths simultaneously. Different computational paths may take different numbers of computational steps. A quantum computer is, therefore, generally unsure whether a subroutine has been completed or not. We do not have a satisfactory resolution to those subtle issues in the general case. Of course, the sender can always avoid this problem by adding redundancies (i.e., adding enough zeroes to the codewords to make them into a fixed length). However, such a prescription is highly inefficient and is self-defeating for our purpose of efficient quantum coding. For this reason, we reject such a prescription in our current discussion.

In the hope of saving resources, the natural next step to try is to stack the signals in line in a single tape during the transmission. To greatly simplify our discussion we shall suppose 