Typical subspace

In quantum information theory, the idea of a typical subspace plays an important role in the proofs of many coding theorems (the most prominent example being Schumacher compression). Its role is analogous to that of the typical set in classical information theory. In quantum information theory, the idea of a typical subspace plays an important role in the proofs of many coding theorems (the most prominent example being Schumacher compression). Its role is analogous to that of the typical set in classical information theory. Consider a density operator ρ {displaystyle ho } with the following spectral decomposition: The weakly typical subspace is defined as the span of all vectors such thatthe sample entropy H ¯ ( x n ) {displaystyle {overline {H}}left(x^{n} ight)} of their classicallabel is close to the true entropy H ( X ) {displaystyle Hleft(X ight)} of the distribution p X ( x ) {displaystyle p_{X}left(x ight)} :