Giovannetti, Vittorio; Lloyd, Seth Additivity properties of a Gaussian channel. (English) Zbl 1232.81013 Phys. Rev. A (3) 69, No. 6, Article ID 062307, 9 p. (2004). Summary: The Amosov-Holevo-Werner conjecture implies the additivity of the minimum Rényi entropies at the output of a channel. The conjecture is proven true for all Rényi entropies of integer order greater than two in a class of Gaussian bosonic channels where the input signal is randomly displaced or where it is coupled linearly to an external environment. Cited in 12 Documents MSC: 81P94 Quantum cryptography (quantum-theoretic aspects) 94A40 Channel models (including quantum) in information and communication theory 81P15 Quantum measurement theory, state operations, state preparations PDFBibTeX XMLCite \textit{V. Giovannetti} and \textit{S. Lloyd}, Phys. Rev. A (3) 69, No. 6, Article ID 062307, 9 p. (2004; Zbl 1232.81013) Full Text: DOI arXiv References: [1] M. A. Nielsen, in: Quantum Computation and Quantum Information (2000) · Zbl 1049.81015 [2] DOI: 10.1109/18.720553 · Zbl 1099.81501 [3] A. S. Holevo, Probl. Inf. Transm. 9 pp 177– (1973) ISSN: http://id.crossref.org/issn/0032-9460 [4] DOI: 10.1109/18.651037 · Zbl 0897.94008 [5] DOI: 10.1103/PhysRevA.54.1869 [6] DOI: 10.1103/PhysRevA.56.131 [7] DOI: 10.1103/PhysRevLett.78.3217 · Zbl 0944.81008 [8] DOI: 10.1103/PhysRevLett.92.027902 [9] DOI: 10.1109/TIT.2002.806153 · Zbl 1063.94028 [10] DOI: 10.1109/18.904522 · Zbl 1016.94012 [11] G. G. Amosov, Probl. Inf. Transm. 36 pp 305– (2000) ISSN: http://id.crossref.org/issn/0032-9460 [12] DOI: 10.1023/A:1025128024427 · Zbl 1030.94022 [13] C. Beck, in: Thermodynamics of Chaotic Systems (1993) [14] DOI: 10.1137/S0040585X97979500 · Zbl 1040.81005 [15] DOI: 10.1103/PhysRevA.59.1820 [16] M. Sohma, Recent Res. Dev. Opt. 1 pp 146– (2000) [17] DOI: 10.1103/PhysRevA.63.032312 [18] DOI: 10.1103/PhysRevA.65.022319 [19] U. Grenander, in: Toeplitz Forms and Their Applications (1958) · Zbl 0080.09501 [20] D. F. Walls, in: Quantum Optics (1994) [21] I. S. Gradshteyn, in: Table of Integrals, Series, and Products (2000) · Zbl 0981.65001 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.