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The additivity of the minimal output entropy and that of the $\chi$-capacity are known to be equivalent for finite-dimensional irreducibly covariant channels.
A. S. Holevo, M. Sohma, O. Hirota, “Error exponents for quantum channels with constrained inputs,” Rep. Math. Phys., 46
2000
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P. W. Shor, “Equivalence of additivity questions in quantum information theory,” Comm. Math. Phys. 246
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A. S. Holevo, “Additivity conjecture and covariant channels,” Int. J. Quant. Inform., 3
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A. S. Holevo and M. E. Shirokov, “Continuous ensembles and the χ \chi -capacity of infinite-dimensional channels,” Probab. Theory and Appl. 50
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M. M. Wolf, “A not-so-normal mode decomposition,” arXiv:0707.0604 (2007)
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M. B. Hastings, “A counterexample to additivity of minimum output entropy,” Nat. Phys., 5
2009
Cited alongside, same era.
M. E. Shirokov, “Continuity of the von Neumann entropy,” Comm. Math. Phys. 296
2010
Cited alongside, same era.
A. S. Holevo and V. Giovannetti, “Quantum channels and their entropic characteristics,” Rep. Prog. Phys. 75
2012
Cited alongside, same era.
A. S. Holevo, Quantum systems, channels, information. A mathematical introduction
2012
Cited alongside, same era.
J. Schäfer, E. Karpov, R. García-Patrón, O. V. Pilyavets, and N. J. Cerf, “Equivalence Relations for the Classical Capacity of Single-Mode Gaussian Quantum Channels,” Phys. Rev. Lett., 111
2013
Later among the works it cites.
V. Giovannetti, R. Garcia-Patron, N. J. Cerf, A. S. Holevo, “Ultimate classical communication rates of quantum optical channels,” Nat. Phot. 8
2014
Closest in time.
A. Mari, V. Giovannetti, and A. S. Holevo, “Quantum state majorization at the output of bosonic Gaussian channels,” Nat. Comm., 5
2014
Closest in time.
V.Giovannetti, A.S.Holevo, R.Garcia-Patron, “A solution of Gaussian optimizer conjecture for quantum channels,” Comm. Math. Phys. 334
2015
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