Related papers: Error Exponents in Quantum Hypothesis Testing

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This paper has been withdrawn by the author due to errors.

This paper has been withdrawn by the author due to a crucial sign error.

This paper has been withdrawn by the author due to a crucial sign error in equation 1.

The paper has been withdrawn due to a crucial error in section 3.

The paper has been withdrawn by the author due to a gap in Proof of Theorem 1.1.

This paper has been withdrawn by the author because the conclusions reached in it are incorrect.

This paper has been withdrawn by the authors, due a crucial error in Sec. 3.

This paper has been withdrawn by the author due a few mistakes in the paper.

The paper has been withdrawn by the author due to a crucial error.

This paper has been withdrawn by the author due to an error in the last paragraph of step 2 of the main proof, on page 6.

The paper has been withdrawn due to numerical error.

This paper was withdrawn by the author.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This paper has been withdrawn by the author due to a crucial mistakes.

This paper has been withdrawn by the author due to serious flaws in certain proofs. For instance, the method used to construct certain automorphic representations is flawed.

This paper is being withdrawn because an error was discovered in lemma 4.3. Although the rest of the paper appears to be correct, this error invalidates the proof of theorem 3.1 and theorem 3.3.

This paper has been withdrawn by the author, due a crucial mistake in proof of lemma 4.2.

This paper has been withdrawn by the authors due to a fatal flaw in the central proof.

This paper has been withdrawn by the author, due to a crucial error in the proof of Thm.1