dorsal/arxiv
View SchemaUniversal Compression of Ergodic Quantum Sources
| Authors | Alexei Kaltchenko, En-Hui Yang |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0302174 |
| URL | https://arxiv.org/abs/quant-ph/0302174 |
Abstract
For a real number $r>0$, let $F(r)$ be the family of all stationary ergodic quantum sources with von Neumann entropy rates less than $r$. We prove that, for any $r>0$, there exists a blind, source-independent block compression scheme which compresses every source from $F(r)$ to $r n$ qubits per input block length $n$ with arbitrarily high fidelity for all large $n$. As our second result,we show that the stationarity and the ergodicity of a quantum source $\{\rho_m \}_{m=1}^{\infty}$ are preserved by any trace-preserving completely positive linear map of the tensor product form ${\cal E}^{\otimes m}$, where a copy of ${\cal E}$ acts locally on each spin lattice site. We also establish ergodicity criteria for so called classically-correlated quantum sources.
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"abstract": "For a real number $r\u003e0$, let $F(r)$ be the family of all stationary ergodic\nquantum sources with von Neumann entropy rates less than $r$. We prove that,\nfor any $r\u003e0$, there exists a blind, source-independent block compression\nscheme which compresses every source from $F(r)$ to $r n$ qubits per input\nblock length $n$ with arbitrarily high fidelity for all large $n$. As our\nsecond result,we show that the stationarity and the ergodicity of a quantum\nsource $\\{\\rho_m \\}_{m=1}^{\\infty}$ are preserved by any trace-preserving\ncompletely positive linear map of the tensor product form ${\\cal E}^{\\otimes\nm}$, where a copy of ${\\cal E}$ acts locally on each spin lattice site. We also\nestablish ergodicity criteria for so called classically-correlated quantum\nsources.",
"arxiv_id": "quant-ph/0302174",
"authors": [
"Alexei Kaltchenko",
"En-Hui Yang"
],
"categories": [
"quant-ph"
],
"title": "Universal Compression of Ergodic Quantum Sources",
"url": "https://arxiv.org/abs/quant-ph/0302174"
},
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"type": "Model",
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