dorsal/arxiv
View SchemaEntropic bounds on coding for noisy quantum channels
| Authors | Nicolas J. Cerf |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9707023 |
| URL | https://arxiv.org/abs/quant-ph/9707023 |
| DOI | 10.1103/PhysRevA.57.3330 |
| Journal | Phys.Rev.A57:3330,1998 |
Abstract
In analogy with its classical counterpart, a noisy quantum channel is characterized by a loss, a quantity that depends on the channel input and the quantum operation performed by the channel. The loss reflects the transmission quality: if the loss is zero, quantum information can be perfectly transmitted at a rate measured by the quantum source entropy. By using block coding based on sequences of n entangled symbols, the average loss (defined as the overall loss of the joint n-symbol channel divided by n, when n tends to infinity) can be made lower than the loss for a single use of the channel. In this context, we examine several upper bounds on the rate at which quantum information can be transmitted reliably via a noisy channel, that is, with an asymptotically vanishing average loss while the one-symbol loss of the channel is non-zero. These bounds on the channel capacity rely on the entropic Singleton bound on quantum error-correcting codes [Phys. Rev. A 56, 1721 (1997)]. Finally, we analyze the Singleton bounds when the noisy quantum channel is supplemented with a classical auxiliary channel.
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"abstract": "In analogy with its classical counterpart, a noisy quantum channel is\ncharacterized by a loss, a quantity that depends on the channel input and the\nquantum operation performed by the channel. The loss reflects the transmission\nquality: if the loss is zero, quantum information can be perfectly transmitted\nat a rate measured by the quantum source entropy. By using block coding based\non sequences of n entangled symbols, the average loss (defined as the overall\nloss of the joint n-symbol channel divided by n, when n tends to infinity) can\nbe made lower than the loss for a single use of the channel. In this context,\nwe examine several upper bounds on the rate at which quantum information can be\ntransmitted reliably via a noisy channel, that is, with an asymptotically\nvanishing average loss while the one-symbol loss of the channel is non-zero.\nThese bounds on the channel capacity rely on the entropic Singleton bound on\nquantum error-correcting codes [Phys. Rev. A 56, 1721 (1997)]. Finally, we\nanalyze the Singleton bounds when the noisy quantum channel is supplemented\nwith a classical auxiliary channel.",
"arxiv_id": "quant-ph/9707023",
"authors": [
"Nicolas J. Cerf"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.57.3330",
"journal_ref": "Phys.Rev.A57:3330,1998",
"title": "Entropic bounds on coding for noisy quantum channels",
"url": "https://arxiv.org/abs/quant-ph/9707023"
},
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