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The Data Compression Theorem for Ergodic Quantum Information Sources
[article]

2003
*
arXiv
*
pre-print

We extend

arXiv:quant-ph/0301043v1
fatcat:ideltecajfdwneqijwijat7vze
*the**data**compression**theorem*to*the*case of*ergodic**quantum**information**sources*. ...*The*rate of this*compression*scheme is equal to*the*von Neumann entropy rate. ...*The*authors are grateful to Ruedi Seiler, Rainer Siegmund-Schultze and Tyll Krüger*for*helpful discussions and valuable comments on this paper. ...##
###
The Data Compression Theorem for Ergodic Quantum Information Sources

2005
*
Quantum Information Processing
*

We extend

doi:10.1007/s11128-003-3195-1
fatcat:bj4uxclth5ewrguv7h5t4wcloy
*the**data**compression**theorem*to*the*case of*ergodic**quantum**information**sources*. ...*The*rate of this*compression*scheme is equal to*the*von Neumann entropy rate. * ...*The*authors are grateful to Ruedi Seiler, Rainer Siegmund-Schultze and Tyll Krüger*for*helpful discussions and valuable comments on this paper. ...##
###
Smooth Rényi Entropy of Ergodic Quantum Information Sources

2007
*
2007 IEEE International Symposium on Information Theory
*

We will actually consider

doi:10.1109/isit.2007.4557235
dblp:conf/isit/SchoenmakersTTV07
fatcat:z2he5ftj3nfovcfwdjhga7a3au
*ergodic**quantum**information**sources*, of which*ergodic*classical*information**sources*are a special case. ... entropy rate*for*a*quantum**source*. ... ACKNOWLEDGMENT Boris Skoric is gratefully acknowledged*for*discussions in*the*early stage of this work. ...##
###
Page 3651 of Mathematical Reviews Vol. , Issue 99e
[page]

1999
*
Mathematical Reviews
*

*For*this extended context- tree weighting algorithm we show that with probability one

*the*

*compression*ratio is not larger than

*the*

*source*entropy

*for*

*source*sequence length T — oo

*for*stationary and

*ergodic*... A sufficient condition

*for*

*information*

*sources*, ensuring decoder self-synchronisation

*for*

*the*T-encoded ...

##
###
Smooth Rényi Entropy of Ergodic Quantum Information Sources
[article]

2007
*
arXiv
*
pre-print

and

arXiv:0704.3504v1
fatcat:3rlqplmb3ng37ffjukhufv5wcq
*the*von Neumann entropy rate*for*a*quantum**information**source*. ... We prove that*the*average smooth Renyi entropy rate will approach*the*entropy rate of a stationary,*ergodic**information**source*, which is equal to*the*Shannon entropy rate*for*a classical*information**source*... Clearly,*the**quantum*AEP*for**ergodic**sources*implies*the*classical AEP*for**ergodic**sources*. ...##
###
Page 2258 of Mathematical Reviews Vol. , Issue 99c
[page]

1991
*
Mathematical Reviews
*

99c:94014

*data**compression*. {*For**the*entire collection see MR 98m:94002.} ...*The*estimators are Cesaro averages of longest match-lengths, and their consistency follows from a generalized*ergodic**theorem*due to Maker. ...##
###
The Shannon-McMillan Theorem for Ergodic Quantum Lattice Systems
[article]

2002
*
arXiv
*
pre-print

*The*one-dimensional case covers

*quantum*

*information*

*sources*and is basic

*for*coding

*theorems*. ...

*The*

*theorem*demonstrates

*the*significance of

*the*von Neumann entropy

*for*translation invariant

*ergodic*

*quantum*spin systems on n-dimensional lattices:

*the*entropy gives

*the*logarithm of

*the*essential number ... We want to express our deep thanks to Ruedi Seiler who emphasized

*the*relevance of a

*quantum*version of

*the*Shannon-McMillan

*theorem*to us. ...

##
###
Second-Order Asymptotics of Visible Mixed Quantum Source Coding via Universal Codes

2016
*
IEEE Transactions on Information Theory
*

Our results provide

doi:10.1109/tit.2016.2571662
fatcat:l6jenaf4nng6ne5ulpslqd4t3u
*the*first example of second order asymptotics*for*a*quantum**information*-processing task employing a resource with memory. ...*The*simplest example of a*quantum**information**source*with memory is a mixed*source*which emits signals entirely from one of two memoryless*quantum**sources*with given a priori probabilities. ... Acknowledgements We would like to thank Vincent Tan*for*useful discussions, and*the*anonymous referees*for*helpful feedback. ...##
###
Page 3377 of Mathematical Reviews Vol. , Issue 97E
[page]

1997
*
Mathematical Reviews
*

It is an approximate fixed-length string matching

*data**compression*combined with a block-coder based on*the*empirical distribution. ... (IL-TLAVH-CME; Holon) Optimal*data**compression*algorithm. (English summary) Comput. Math. Appl. 32 (1996), no. 5, 57-72. ...##
###
Guest editorial

1998
*
IEEE Transactions on Information Theory
*

*The*timely tutorial survey of

*quantum*

*information*theory by Bennett and Shor gives an accessible introduction to

*compression*, transmission and cryptography

*for*quantummechanical models. ... Csiszár gives an overview of

*the*basic tools and achievements of this method. Determining

*the*fundamental limits of

*sources*and channels with memory often calls

*for*

*ergodic*-theoretic tools. ...

##
###
Fifty years of Shannon theory

1998
*
IEEE Transactions on Information Theory
*

A brief chronicle is given of

doi:10.1109/18.720531
fatcat:gj4lp6rgtza5bd6becmv3kx2zu
*the*historical development of*the*central problems in*the*theory of fundamental limits of*data**compression*and reliable communication. ... Unlike memoryless*sources*,*for*which*the*AEP is equivalent to*the*weak law of large numbers, showing that*the*AEP is satisfied*for*stationary*ergodic**sources*requires a nontrivial use of*the**ergodic**theorem*... Because of its relevance to*data**compression*, it is natural to investigate whether*Theorem*3 applies to*sources*with memory. ...##
###
Fifty Years of Shannon Theory
[chapter]

2009
*
Information Theory
*

A brief chronicle is given of

doi:10.1109/9780470544907.ch2
fatcat:h22tqdqxsjcblhwqvrphmwzvhu
*the*historical development of*the*central problems in*the*theory of fundamental limits of*data**compression*and reliable communication. ... Unlike memoryless*sources*,*for*which*the*AEP is equivalent to*the*weak law of large numbers, showing that*the*AEP is satisfied*for*stationary*ergodic**sources*requires a nontrivial use of*the**ergodic**theorem*... Because of its relevance to*data**compression*, it is natural to investigate whether*Theorem*3 applies to*sources*with memory. ...##
###
Data compression limit for an information source of interacting qubits
[article]

2002
*
arXiv
*
pre-print

We establish

arXiv:quant-ph/0207069v2
fatcat:hbtlh73wt5blxar7zpyh5jxawe
*the*limit*for**the**compression*of*information*from such a*source*and show that asymptotically it is given by*the*von Neumann entropy rate. ... Our result can be viewed as a*quantum*analog of Shannon's noiseless coding*theorem**for*a class of non - i.i.d.*quantum**information**sources*. ... Hence,*the**data**compression*limit,*for**the*class of non-i.i.d.*quantum**information**sources*considered in this paper, is given by*the*von Neumann entropy rate h. ...##
###
Page 7263 of Mathematical Reviews Vol. , Issue 2003i
[page]

2003
*
Mathematical Reviews
*

This is analogous to

*the*Kraft in- equality in lossless*data**compression*. In*the*case of stationary*ergodic**sources*our results reduce to*the*classical coding theo- rems. ... In*the*present paper*the*authors show that*for**the**quantum*channel ®(p) = a4 (Tr(p)l - p") in*the*Hilbert space H, dim H = d > 3,*the*multiplicativity conjecture is not valid*for*two copies of this channel ...##
###
A Quantum Version of Sanov's Theorem

2005
*
Communications in Mathematical Physics
*

We present a

doi:10.1007/s00220-005-1426-2
fatcat:nzd6hhrvebdvbbv4ywde3cyyeq
*quantum*extension of a version of Sanov's*theorem*focussing on a hypothesis testing aspect of*the**theorem*: There exists a sequence of typical subspaces*for*a given set Ψ of stationary*quantum*... Analogously to*the*classical case,*the*exponential separating rate is equal to*the*infimum of*the**quantum*relative entropy with respect to*the**quantum*reference state over*the*set Ψ. ... This work was supported by*the*DFG via*the*project "Entropie, Geometrie und Kodierung großer Quanten-Informationssysteme", by*the*ESF via*the*project "Belearning" at*the*TU Berlin and*the*DFG-Forschergruppe ...
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