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But — and this is another reason for studying quantum information theory — such considerations are also giving us a new perspective on quantum theory, which may in time lead to a set of principles from which this theory can be derived. One of the major new perspectives presented by quantum information theory is the idea of analysing quantum theory from within. Often such analyses take the form of algorithms or cyclic processes, or in some circumstances even games [17]; in short, the situations considered are finite and completely specified.

And of course, since almost all the codes are typical, we can choose the code so that the letter frequencies of the code are close to those of the original ensemble. The resulting code will consist of nS(ρ) codewords which are almost equally likely; thus S(ρ) bits are communicated per quantum system received. It is interesting to note how this communication is achieved: as the number of signals becomes large, it becomes possible to choose words which are almost orthogonal and hence highly distinguishable.

L S M-1 P M-1 SM Letters P1 C2 P2 C3 P3 C4 P4 . . . . . 2: A schematic representation of random codes and their probabilities averaged over all codes, we can calculate the error only for these typical codes and include an arbitrarily small ǫ-error for the contribution from non-typical codes. To calculate this error, note that the expected overlap of any two code words |u = |φx1 . . |φxn and |v = |φy1 . . |φyn is E | u|v |2 = x1 ,... ,xn y1 ,... ,yn px1 py1 . . pxn pyn | φx1 |φy1 |2 .

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