Degradable channels, less noisy channels, and quantum statistical morphisms: An equivalence relation
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Two partial orderings among communication channels, namely “being degradable into” and “being less noisy than,” are reconsidered in the light of recent results about statistical comparisons of quantum channels. Though our analysis covers at once both classical and quantum channels, we also provide a separate treatment of classical noisy channels and show how in this case an alternative self-contained proof can be constructed, with its own particular merits with respect to the general result.
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- 5.Körner, J. and Marton, K., Comparison of Two Noisy Channels, Topics in Information Theory (2nd Colloq., Keszthely, Hungary, 1975), Csiszár, I. and Elias, P., Eds., Colloq. Math. Soc. János Bolyai, vol. 16, Amsterdam: North-Holland, 1977, pp. 411–423.Google Scholar
- 6.El Gamal, A.A., Broadcast Channels with and without Feedback, Proc. 11th Asilomar Conference on Circuits, Systems and Computers, Pacific Grove, CA, Nov. 7–9, 1977, Chan, S.-P., Ed., New York: IEEE, 1978, pp. 180–183.Google Scholar
- 14.Chefles, A., The Quantum Blackwell Theorem and Minimum Error State Discrimination, arXiv:0907. 0866v4 [quant-ph], 2009.Google Scholar
- 18.Matsumoto, K., An Example of a Quantum Statistical Model Which Cannot Be Mapped to a Less Informative One by Any Trace Preserving Positive Map, arXiv:1409.5658 [quant-ph, math.ST], 2014.Google Scholar
- 25.Buscemi, F., Fully Quantum Second-Law-like Statements from the Theory of Statistical Comparisons, arXiv:1505.00535 [quant-ph], 2014.Google Scholar