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Moreover, we were able to prove the coding theorem for arbitrary I with informed decoder. It is important to remark here that we used a different notion of codes in , following , which is motivated by the theory of quantum error correction. In the cases of an informed decoder and uninformed users this change does not appear to be of importance. In the case of an informed encoder it is of crucial importance in the proof of the direct part of the coding result. In our former paper, the strategy of proof was as follows.
Chem. Phys. 108(4), 1429–1433 (1998) 54 A. Laptev, O. Safronov 11. : Maximum properties and inequalities for the eigenvalues of completely continuous operators. Proc. Nat. Acad. , U. S. A. 37, 760–766 (1951) 12. : Inequalities for the moments of the eigenvalues of the Schrödinger Hamiltonian and their relation to Sobolev inequalities. In: Studies in Mathematical Physics (Essays in Honor of Valentine Bargmann), Princeton, NJ: Princeton Univ. Press, 1976, pp. 269–303 13. : Tunneling with dissipation.
We determine the entanglement transmission and entanglement-generating capacities of compound quantum channels and show that they are equal. Moreover, we investigate two variants of that basic scenario, namely the cases of informed decoder or informed encoder, and derive corresponding capacity results. Contents 1. 2. 3. 4. 5. 6. 7. Introduction . . . . . . . . . . . . . . . . . Definitions and Main Result . . . . . . . . . . . . . One-Shot Results . . . . . . .