dorsal/arxiv
View SchemaOn the von Neumann capacity of noisy quantum channels
| Authors | C. Adami, N. J. Cerf |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9609024 |
| URL | https://arxiv.org/abs/quant-ph/9609024 |
| DOI | 10.1103/PhysRevA.56.3470 |
| Journal | Phys.Rev.A56:3470,1997 |
Abstract
We discuss the capacity of quantum channels for information transmission and storage. Quantum channels have dual uses: they can be used to transmit known quantum states which code for classical information, and they can be used in a purely quantum manner, for transmitting or storing quantum entanglement. We propose here a definition of the von Neumann capacity of quantum channels, which is a quantum mechanical extension of the Shannon capacity and reverts to it in the classical limit. As such, the von Neumann capacity assumes the role of a classical or quantum capacity depending on the usage of the channel. In analogy to the classical construction, this capacity is defined as the maximum von Neumann mutual entropy processed by the channel, a measure which reduces to the capacity for classical information transmission through quantum channels (the "Kholevo capacity") when known quantum states are sent. The quantum mutual entropy fulfills all basic requirements for a measure of information, and observes quantum data-processing inequalities. We also derive a quantum Fano inequality relating the quantum loss of the channel to the fidelity of the quantum code. The quantities introduced are calculated explicitly for the quantum "depolarizing" channel. The von Neumann capacity is interpreted within the context of superdense coding, and an "extended" Hamming bound is derived that is consistent with that capacity.
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"abstract": "We discuss the capacity of quantum channels for information transmission and\nstorage. Quantum channels have dual uses: they can be used to transmit known\nquantum states which code for classical information, and they can be used in a\npurely quantum manner, for transmitting or storing quantum entanglement. We\npropose here a definition of the von Neumann capacity of quantum channels,\nwhich is a quantum mechanical extension of the Shannon capacity and reverts to\nit in the classical limit. As such, the von Neumann capacity assumes the role\nof a classical or quantum capacity depending on the usage of the channel. In\nanalogy to the classical construction, this capacity is defined as the maximum\nvon Neumann mutual entropy processed by the channel, a measure which reduces to\nthe capacity for classical information transmission through quantum channels\n(the \"Kholevo capacity\") when known quantum states are sent. The quantum mutual\nentropy fulfills all basic requirements for a measure of information, and\nobserves quantum data-processing inequalities. We also derive a quantum Fano\ninequality relating the quantum loss of the channel to the fidelity of the\nquantum code. The quantities introduced are calculated explicitly for the\nquantum \"depolarizing\" channel. The von Neumann capacity is interpreted within\nthe context of superdense coding, and an \"extended\" Hamming bound is derived\nthat is consistent with that capacity.",
"arxiv_id": "quant-ph/9609024",
"authors": [
"C. Adami",
"N. J. Cerf"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.56.3470",
"journal_ref": "Phys.Rev.A56:3470,1997",
"title": "On the von Neumann capacity of noisy quantum channels",
"url": "https://arxiv.org/abs/quant-ph/9609024"
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