Smooth Rényi entropy of ergodic quantum information sources

B. Schoenmakers; J. Tjoelker; P.T. Tuyls; E.A. Verbitskiy

doi:10.1109/ISIT.2007.4557235

Smooth Rényi entropy of ergodic quantum information sources

B. Schoenmakers
, J. Tjoelker
, P.T. Tuyls
, E.A. Verbitskiy

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

8 Citations (Scopus)

4 Downloads (Pure)

Abstract

We investigate the recently introduced notion of smooth Rényi entropy for the case of ergodic information sources, thereby generalizing previous work which concentrated mainly on i.i.d. information sources. We will actually consider ergodic quantum information sources, of which ergodic classical information sources are a special case. We prove that the average smooth Rényi entropy rate will approach the entropy rate of a stationary, ergodic source, which is equal to the Shannon entropy rate for a classical source and the von Neumann entropy rate for a quantum source.

Original language	English
Title of host publication	Proceedings 2007 IEEE International Symposium on Information Theory (ISIT 2007) 24-29 June 2007, Nice, France
Place of Publication	Piscataway NJ
Publisher	Institute of Electrical and Electronics Engineers
Pages	256-260
ISBN (Print)	978-1-4244-1397-3
DOIs	https://doi.org/10.1109/ISIT.2007.4557235
Publication status	Published - 2007
Event	2007 IEEE International Symposium on Information Theory, ISIT 2007 - Nice, France Duration: 24 Jun 2007 → 29 Jun 2007

Conference

Conference	2007 IEEE International Symposium on Information Theory, ISIT 2007
Country/Territory	France
City	Nice
Period	24/06/07 → 29/06/07
Other	ISIT 2007, Nice, France

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10.1109/ISIT.2007.4557235

Cite this

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title = "Smooth R{\'e}nyi entropy of ergodic quantum information sources",

abstract = "We investigate the recently introduced notion of smooth R{\'e}nyi entropy for the case of ergodic information sources, thereby generalizing previous work which concentrated mainly on i.i.d. information sources. We will actually consider ergodic quantum information sources, of which ergodic classical information sources are a special case. We prove that the average smooth R{\'e}nyi entropy rate will approach the entropy rate of a stationary, ergodic source, which is equal to the Shannon entropy rate for a classical source and the von Neumann entropy rate for a quantum source.",

author = "B. Schoenmakers and J. Tjoelker and P.T. Tuyls and E.A. Verbitskiy",

year = "2007",

doi = "10.1109/ISIT.2007.4557235",

language = "English",

isbn = "978-1-4244-1397-3",

pages = "256--260",

booktitle = "Proceedings 2007 IEEE International Symposium on Information Theory (ISIT 2007) 24-29 June 2007, Nice, France",

publisher = "Institute of Electrical and Electronics Engineers",

address = "United States",

note = "2007 IEEE International Symposium on Information Theory, ISIT 2007 ; Conference date: 24-06-2007 Through 29-06-2007",

}

Schoenmakers, B, Tjoelker, J, Tuyls, PT & Verbitskiy, EA 2007, Smooth Rényi entropy of ergodic quantum information sources. in Proceedings 2007 IEEE International Symposium on Information Theory (ISIT 2007) 24-29 June 2007, Nice, France. Institute of Electrical and Electronics Engineers, Piscataway NJ, pp. 256-260, 2007 IEEE International Symposium on Information Theory, ISIT 2007, Nice, France, 24/06/07. https://doi.org/10.1109/ISIT.2007.4557235

Smooth Rényi entropy of ergodic quantum information sources. / Schoenmakers, B.; Tjoelker, J.; Tuyls, P.T. et al.
Proceedings 2007 IEEE International Symposium on Information Theory (ISIT 2007) 24-29 June 2007, Nice, France. Piscataway NJ: Institute of Electrical and Electronics Engineers, 2007. p. 256-260.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

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T1 - Smooth Rényi entropy of ergodic quantum information sources

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AU - Tjoelker, J.

AU - Tuyls, P.T.

AU - Verbitskiy, E.A.

PY - 2007

Y1 - 2007

N2 - We investigate the recently introduced notion of smooth Rényi entropy for the case of ergodic information sources, thereby generalizing previous work which concentrated mainly on i.i.d. information sources. We will actually consider ergodic quantum information sources, of which ergodic classical information sources are a special case. We prove that the average smooth Rényi entropy rate will approach the entropy rate of a stationary, ergodic source, which is equal to the Shannon entropy rate for a classical source and the von Neumann entropy rate for a quantum source.

AB - We investigate the recently introduced notion of smooth Rényi entropy for the case of ergodic information sources, thereby generalizing previous work which concentrated mainly on i.i.d. information sources. We will actually consider ergodic quantum information sources, of which ergodic classical information sources are a special case. We prove that the average smooth Rényi entropy rate will approach the entropy rate of a stationary, ergodic source, which is equal to the Shannon entropy rate for a classical source and the von Neumann entropy rate for a quantum source.

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DO - 10.1109/ISIT.2007.4557235

M3 - Conference contribution

SN - 978-1-4244-1397-3

SP - 256

EP - 260

BT - Proceedings 2007 IEEE International Symposium on Information Theory (ISIT 2007) 24-29 June 2007, Nice, France

PB - Institute of Electrical and Electronics Engineers

CY - Piscataway NJ

T2 - 2007 IEEE International Symposium on Information Theory, ISIT 2007

Y2 - 24 June 2007 through 29 June 2007

ER -

Smooth Rényi entropy of ergodic quantum information sources

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