Related papers: Gallager Bound of Classical-Quantum Channel Coding

This paper has been withdrawn by the author due to a crucial error.

This paper has been withdrawn by the author due to a crucial sign error in equation 1

This paper has been withdrawn due to an error in section 3.

This paper has been withdrawn by the author. Lemma 8 is used in the proof of Lemma 6, but it is not correct. Lemma 6 is essential for the main results.

This paper has been withdrawn by the author due to a mistake.

The paper has been withdrawn by the author due to crucial error in formula (14) which does not satisfy conditions for S(x,y) domain if only d>2.

Paper withdrawn due to a crucial algebraic error in section 3.

This paper has been withdrawn by the author because the arguments presented in the paper is incomplete.

This paper has been withdrawn by the author due to a crucial error in the last lines in the proof of Lemma 3.3.

This paper has been withdrawn by the author due to a crucial error in the formulation.

This paper has been withdrawn by the authors due to some fatal errors in the analysis.

This paper has been withdrawn by the author because there are some typos in proofs.

This paper was withdrawn by the author. It turns out that similar ideas have been presented before. The author apologizes.

This paper has been withdrawn by the author due to an error.

This paper has been withdrawn by the author due to an erro thereon line -2 of page 4.

This paper has been withdrawn by the author due to a crucial sign error in equation 2.

This paper has been withdrawn by the author, due to an error in relation (11).

This paper has been withdrawn by the author due to a crucial sign error in Proposition 3.1.

This paper has been withdrawn by the author.

This paper has been withdrawn by the author due a few mistakes in the paper.