Lossless quantum data compression with exponential penalization: An operational interpretation of the quantum Rényi entropy

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. The...

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Detalles Bibliográficos
Publicado: 2017
Materias:
entropy
information processing
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_20452322_v7_n1_p_Bellomo
http://hdl.handle.net/20.500.12110/paper_20452322_v7_n1_p_Bellomo
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
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spelling paper:paper_20452322_v7_n1_p_Bellomo2023-06-08T16:33:29Z Lossless quantum data compression with exponential penalization: An operational interpretation of the quantum Rényi entropy entropy information processing 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). 2017 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_20452322_v7_n1_p_Bellomo http://hdl.handle.net/20.500.12110/paper_20452322_v7_n1_p_Bellomo
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic entropy
information processing
spellingShingle entropy
information processing
Lossless quantum data compression with exponential penalization: An operational interpretation of the quantum Rényi entropy
topic_facet entropy
information processing
description 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).
title Lossless quantum data compression with exponential penalization: An operational interpretation of the quantum Rényi entropy
title_short Lossless quantum data compression with exponential penalization: An operational interpretation of the quantum Rényi entropy
title_full Lossless quantum data compression with exponential penalization: An operational interpretation of the quantum Rényi entropy
title_fullStr Lossless quantum data compression with exponential penalization: An operational interpretation of the quantum Rényi entropy
title_full_unstemmed Lossless quantum data compression with exponential penalization: An operational interpretation of the quantum Rényi entropy
title_sort lossless quantum data compression with exponential penalization: an operational interpretation of the quantum rényi entropy
publishDate 2017
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_20452322_v7_n1_p_Bellomo
http://hdl.handle.net/20.500.12110/paper_20452322_v7_n1_p_Bellomo
_version_ 1768543679205605376

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