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Abstract:

Based on the problem of quantum data compression in a lossless way, we present here an operational interpretation for the family of quantum Rényi entropies. In order to do this, we appeal to a very general quantum encoding scheme that satisfies a quantum version of the Kraft-McMillan inequality. Then, in the standard situation, where one is intended to minimize the usual average length of the quantum codewords, we recover the known results, namely that the von Neumann entropy of the source bounds the average length of the optimal codes. Otherwise, we show that by invoking an exponential average length, related to an exponential penalization over large codewords, the quantum Rényi entropies arise as the natural quantities relating the optimal encoding schemes with the source description, playing an analogous role to that of von Neumann entropy. © 2017 The Author(s).

Registro:

Documento: Artículo
Título:Lossless quantum data compression with exponential penalization: An operational interpretation of the quantum Rényi entropy
Autor:Bellomo, G.; Bosyk, G.M.; Holik, F.; Zozor, S.
Filiación:CONICET-Universidad de Buenos Aires, Instituto de Investigación en Ciencias de la Computación (ICC), Buenos Aires, Argentina
Instituto de Física La Plata, UNLP, CONICET, Facultad de Ciencias Exactas, Casilla de Correo 67, La Plata, 1900, Argentina
Univ. Grenoble Alpes, CNRS, Grenoble INP Institute of Engineering, GIPSALab, Grenoble, 38000, France
Palabras clave:entropy; information processing
Año:2017
Volumen:7
Número:1
DOI: http://dx.doi.org/10.1038/s41598-017-13350-y
Título revista:Scientific Reports
Título revista abreviado:Sci. Rep.
ISSN:20452322
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_20452322_v7_n1_p_Bellomo

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Citas:

---------- APA ----------
Bellomo, G., Bosyk, G.M., Holik, F. & Zozor, S. (2017) . Lossless quantum data compression with exponential penalization: An operational interpretation of the quantum Rényi entropy. Scientific Reports, 7(1).
http://dx.doi.org/10.1038/s41598-017-13350-y
---------- CHICAGO ----------
Bellomo, G., Bosyk, G.M., Holik, F., Zozor, S. "Lossless quantum data compression with exponential penalization: An operational interpretation of the quantum Rényi entropy" . Scientific Reports 7, no. 1 (2017).
http://dx.doi.org/10.1038/s41598-017-13350-y
---------- MLA ----------
Bellomo, G., Bosyk, G.M., Holik, F., Zozor, S. "Lossless quantum data compression with exponential penalization: An operational interpretation of the quantum Rényi entropy" . Scientific Reports, vol. 7, no. 1, 2017.
http://dx.doi.org/10.1038/s41598-017-13350-y
---------- VANCOUVER ----------
Bellomo, G., Bosyk, G.M., Holik, F., Zozor, S. Lossless quantum data compression with exponential penalization: An operational interpretation of the quantum Rényi entropy. Sci. Rep. 2017;7(1).
http://dx.doi.org/10.1038/s41598-017-13350-y