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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| Formato: | JOUR |
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_20452322_v7_n1_p_Bellomo |
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todo:paper_20452322_v7_n1_p_Bellomo2023-10-03T16:38:18Z Lossless quantum data compression with exponential penalization: An operational interpretation of the quantum Rényi entropy Bellomo, G. Bosyk, G.M. Holik, F. Zozor, S. 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). JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar 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 Bellomo, G. Bosyk, G.M. Holik, F. Zozor, S. 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). |
| format |
JOUR |
| author |
Bellomo, G. Bosyk, G.M. Holik, F. Zozor, S. |
| author_facet |
Bellomo, G. Bosyk, G.M. Holik, F. Zozor, S. |
| author_sort |
Bellomo, G. |
| 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 |
| url |
http://hdl.handle.net/20.500.12110/paper_20452322_v7_n1_p_Bellomo |
| work_keys_str_mv |
AT bellomog losslessquantumdatacompressionwithexponentialpenalizationanoperationalinterpretationofthequantumrenyientropy AT bosykgm losslessquantumdatacompressionwithexponentialpenalizationanoperationalinterpretationofthequantumrenyientropy AT holikf losslessquantumdatacompressionwithexponentialpenalizationanoperationalinterpretationofthequantumrenyientropy AT zozors losslessquantumdatacompressionwithexponentialpenalizationanoperationalinterpretationofthequantumrenyientropy |
| _version_ |
1807323609377538048 |