# Calculating length of code words in quantum information(compression)

I was studying this article by Boestrom and Felbinger.

We define the significant length of the codewords in the preparation of the communication protocol : $$L_c(w_i) = \lceil log_k(i) \rceil$$

We can also calculate the base length of the codewords : $$\underline L _c(x)= \max_{i=1,...,d} \{L_c(w_i) | \ |\langle w_i|x\rangle|^2 > 0 \} \tag{101}$$

After explaining the protocol, they give an explicit example with a source message set : $$\chi = \{|a\rangle,|b\rangle, |c\rangle, |d\rangle, |e\rangle, |f\rangle, |g\rangle, |h\rangle, |i\rangle, |j\rangle \}$$

The Authors then calculate that : $$\underline L _c (a) = 0 ; \underline L _c (b) = \underline L _c (c) = \underline L _c (d) = 1 \tag{136}$$ $$\underline L _c (e) = \underline L _c (f) = \underline L _c (g) = \underline L _c (h) = \underline L _c (i) = \underline L _c (j) =2 \tag{137}$$

I have troubles understanding the equation 101 and how it calculates the length of the strings. Maybe explaining the examples in equations 136 and 137, will help too.

Thanks for reading, hope you can help !

• Can you edit the question to summarize your understanding of the paper, and where you have gotten lost? Presently this question may be too short on details to motivate people looking for answers or ways to help. Apr 19 at 23:25
• One more question are we not storing data when we follow this algorithm? Apr 20 at 18:04
• I edited the question, I did not understand everything completely but I think this is enough to provide context. We can therefor reopen the question. Apr 23 at 8:49