es, representing only about 3% of the codeword space A. Summing the values Np(u) in the table, one finds that the probability of any received codeword belonging to this typical subspace is p(s2) = 0.90208, which is relatively high. This result yields the lower bound 8 = 1 - p(S2) = 0.09792 and hence, using da = 0.8535, the transmission fidelity F = (1 - 8)2 8219 = 0.81859 2 82%, which is fair. From the table, we also find that the maximum value of R, or the best compression factor achievable under this coding scheme, is given by the highest value of E in the subspace S2, namely Emax = 0.29681, or R = 0.89769 2 89%. Having defined the E-typical subspace So (with the choice E < 0.29681), the next step is to analyze the effect of increasing the message length N. It is only a matter of tabulating a spreadsheet that outputs the same data as shown in Table 22.4, along with the values and F = (1 - 8)2 + SN's for each value of n. Care must be taken to effect the summation yielding p(S2) only in the spreadsheet domain where 0< & 0 29681. The fidelity F calculated for message lengths from n = 19 to n = 100 Quantum data compression Table 22.4 Defining an e-typical subspace So with E < 0.29681, in the case n = 19, corresponding to a maximum compression R = 0.89769. Codeword type u Np(u) 21920 4.936 x 10-2 0.37243 0.97330 21821 8.469 x 10-3 1.609 x 10-1 0.23858 0.83946 21722 1.453 x 10-3 2.485 x 10-1 0.10473 0.70561 21623 2.493 x 10-4 2.416 x 10-1 0.02911 0.62999 21521 4.277 x 10-5 1.658 x 10-1 0.16296 0.76384 21425 7.339 x 10-6 11628 8.534 x 10-2 0.29681 0.89769 21326 1.259 x 10-6 27132 0.43066 1.03153 21227 2.160 x 10-7 50388 0.56451 1.16538 21128 3.707 x 10-8 75582 0.69835 1.29923 21029 6.359 x 10-9 92378 0.83220 1.43308 29210 1.091 x 10-9 92378 0.96605 1.56692 28211 1.872 x 10-10 75582 1.09990 1.70077 27212 3.212 x 10-11 50388 1.23375 1.83462 26213 5.511 x 10-12 27132 1.36759 1.96847 9.455 x 10-1 11628 1.50144 2.10232 1.622 x 10-1 1.63529 2.23616 23216 2.783 x 10-1 1.76914 2.37001 22217 4.775 x 10-15 1.90298 2.50386 21218