based on quantum mechanics, a well-tested scientific theory in real experiments. This paper concerns quantum information.

The goal of this paper is to find a quantum source coding scheme analogous to Huffman coding in the classical source coding theory [@Cover]. Let us recapitulate the result of classical theory. Consider the simple example of a memoryless source that emits a sequence of independent, identically distributed signals each of which is chosen from a list $w_1, w_2, \cdots ,w_n$ with probabilities $p_1,
p_2, \cdots, p_n$. The task of source coding is to store such signals with a minimal amount of resources. In classical information theory, resources are measured in bits. A standard coding scheme to use is the optimally efficient Huffman coding algorithm, which is a well-known lossless coding scheme for data compression.

Apart from being highly efficient, it has the advantage of being instantaneous, i.e., unlike block coding schemes, the encoding and decoding of each signal can be done immediately. Note also that codewords of variable lengths are used to achieve efficiency. As we will see below, these two features—instantaneousness and variable length—of Huffman coding are difficult to generalize to the quantum case.

Now let us consider quantum information. In the 