Abstract
In this thesis, we consider the lossless quantum data compression scheme proposed by Boström and Felbinger. We first obtain a lower bound on the average base length of their proposed compression scheme in terms of the eigenvalues of the density operator associated with the quantum source. Then we use this result to derive several new lower bounds on the average base length. When no partial information is available about the dimension of the source space and the eigenvalues of the density operator, we obtain a new lower bound on the average base length in terms of the von Neumann entropy. We next consider the case that only the largest eigenvalue of the density operator is available as side information, and obtain several new lower bounds on the average base length by using the method of Lagrange multiplier. Furthermore, given that the dimension of the source space and/or some eigenvalues of the density operator are available, we derive new lower bounds in terms of the von Neumann entropy and the available side information.