dorsal/arxiv
View SchemaEnergy Requirements for Quantum Data Compression and 1-1 Coding
| Authors | Luke Rallan, Vlatko Vedral |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0208039 |
| URL | https://arxiv.org/abs/quant-ph/0208039 |
| DOI | 10.1103/PhysRevA.68.042309 |
| Journal | PRA, Volume 68, Issue 7, 2003 |
Abstract
By looking at quantum data compression in the second quantisation, we present a new model for the efficient generation and use of variable length codes. In this picture lossless data compression can be seen as the {\em minimum energy} required to faithfully represent or transmit classical information contained within a quantum state. In order to represent information we create quanta in some predefined modes (i.e. frequencies) prepared in one of two possible internal states (the information carrying degrees of freedom). Data compression is now seen as the selective annihilation of these quanta, the energy of whom is effectively dissipated into the environment. As any increase in the energy of the environment is intricately linked to any information loss and is subject to Landauer's erasure principle, we use this principle to distinguish lossless and lossy schemes and to suggest bounds on the efficiency of our lossless compression protocol. In line with the work of Bostr\"{o}m and Felbinger \cite{bostroem}, we also show that when using variable length codes the classical notions of prefix or uniquely decipherable codes are unnecessarily restrictive given the structure of quantum mechanics and that a 1-1 mapping is sufficient. In the absence of this restraint we translate existing classical results on 1-1 coding to the quantum domain to derive a new upper bound on the compression of quantum information. Finally we present a simple quantum circuit to implement our scheme.
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"abstract": "By looking at quantum data compression in the second quantisation, we present\na new model for the efficient generation and use of variable length codes. In\nthis picture lossless data compression can be seen as the {\\em minimum energy}\nrequired to faithfully represent or transmit classical information contained\nwithin a quantum state.\n In order to represent information we create quanta in some predefined modes\n(i.e. frequencies) prepared in one of two possible internal states (the\ninformation carrying degrees of freedom). Data compression is now seen as the\nselective annihilation of these quanta, the energy of whom is effectively\ndissipated into the environment. As any increase in the energy of the\nenvironment is intricately linked to any information loss and is subject to\nLandauer\u0027s erasure principle, we use this principle to distinguish lossless and\nlossy schemes and to suggest bounds on the efficiency of our lossless\ncompression protocol.\n In line with the work of Bostr\\\"{o}m and Felbinger \\cite{bostroem}, we also\nshow that when using variable length codes the classical notions of prefix or\nuniquely decipherable codes are unnecessarily restrictive given the structure\nof quantum mechanics and that a 1-1 mapping is sufficient. In the absence of\nthis restraint we translate existing classical results on 1-1 coding to the\nquantum domain to derive a new upper bound on the compression of quantum\ninformation. Finally we present a simple quantum circuit to implement our\nscheme.",
"arxiv_id": "quant-ph/0208039",
"authors": [
"Luke Rallan",
"Vlatko Vedral"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.68.042309",
"journal_ref": "PRA, Volume 68, Issue 7, 2003",
"title": "Energy Requirements for Quantum Data Compression and 1-1 Coding",
"url": "https://arxiv.org/abs/quant-ph/0208039"
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