dorsal/arxiv
View SchemaConditions for the multiplicativity of maximal l_p-norms of channels for fixed integer p
| Authors | Vittorio Giovannetti, Seth Lloyd, Mary Beth Ruskai |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0408103 |
| URL | https://arxiv.org/abs/quant-ph/0408103 |
| DOI | 10.1063/1.1862094 |
| Journal | J. Math. Phys. 46, 042105 (2005) |
Abstract
We introduce a condition for memoryless quantum channels which, when satisfied guarantees the multiplicativity of the maximal l_p-norm with p a fixed integer. By applying the condition to qubit channels, it can be shown that it is not a necessary condition, although some known results for qubits can be recovered. When applied to the Werner-Holevo channel, which is known to violate multiplicativity when p is large relative to the dimension d, the condition suggests that multiplicativity holds when $d \geqslant 2^{p-1}$. This conjecture is proved explicitly for p=2, 3, 4. Finally, a new class of channels is considered which generalizes the depolarizing channel to maps which are combinations of the identity channel and a noisy one whose image is an arbitrary density matrix. It is shown that these channels are multiplicative for p = 2.
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"abstract": "We introduce a condition for memoryless quantum channels which, when\nsatisfied guarantees the multiplicativity of the maximal l_p-norm with p a\nfixed integer. By applying the condition to qubit channels, it can be shown\nthat it is not a necessary condition, although some known results for qubits\ncan be recovered. When applied to the Werner-Holevo channel, which is known to\nviolate multiplicativity when p is large relative to the dimension d, the\ncondition suggests that multiplicativity holds when $d \\geqslant 2^{p-1}$. This\nconjecture is proved explicitly for p=2, 3, 4. Finally, a new class of channels\nis considered which generalizes the depolarizing channel to maps which are\ncombinations of the identity channel and a noisy one whose image is an\narbitrary density matrix. It is shown that these channels are multiplicative\nfor p = 2.",
"arxiv_id": "quant-ph/0408103",
"authors": [
"Vittorio Giovannetti",
"Seth Lloyd",
"Mary Beth Ruskai"
],
"categories": [
"quant-ph"
],
"doi": "10.1063/1.1862094",
"journal_ref": "J. Math. Phys. 46, 042105 (2005)",
"title": "Conditions for the multiplicativity of maximal l_p-norms of channels for fixed integer p",
"url": "https://arxiv.org/abs/quant-ph/0408103"
},
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