asymptotically decreases. This suggests that given a compression factor n = S(p), the fidelity F asymptotically increases with the message length n. Here, I shall heuristically verify this property by considering messages longer than three qubits, and evaluating the corresponding fidelity, while assuming S(p) = 0.6008 with the eigenvalues da = 0.8535, Ab = 0.1465. The probabilities associated with messages of 4-qubit length (n = 4) are defined in Table 22.1. This table reads as follows. We call "codeword" any 4-qubit with Ai, Nj, Ak, AI = Na, Ab. We call "codeword type" any 4-qubit obtained by per- mutation of the same values Ni, 2j, Ak, A1. Each type has a probability p = hidjakal and a number N given by the associated combinatorics. For instance, the codeword type 12ahahbhby has p=2222 = 0.0156 and N = C2 = 6, as shown in Table 22.1. The product Np, also shown in the table, corresponds to the likelihood of all messages based on a given codeword type. We define the typical space as So = {laadahaha), laadahahb), 12ahahbdb), I }, where <-> stands for all possible permuta- tions of the index i, j, k, 1, corresponding overall to 1 + 4 + 6 = 11 "typical" code- words. We observe from the table that So has a total likelihood of P(S2) = 1 8 = 0.5308 + 0.3643 + 0.0937 = 0.9888, while for the complementary space so the like- lihood is p(s2-) = 8 = 0.0112. Similarly to the definition in Eq. (22.20), we obtain the fidelity: = (0.9888)2 + 0.0112 x (0.8535)4 (22.23) = 0.983. This result compares favourably with the fidelity = 0.923 obtained earlier for the compression of quantum messages of length n = 3, which illustrates the property that fidelity increases with message length. In the case n = 4, however, the compression factor is Nn=4 = =3/4=0.75, which represents less compression than in the previous case, where Nn=3 = 2/3 = 0.66. On the other hand, we cannot compress the 4-qubit message into a 2-qubit one, because [S(p) X 4] = [2.40] = 3 bits, meaning that the minimum length of the compressed message is three qubits. Quan