dorsal/arxiv
View SchemaDecomposition of time-covariant operations on quantum systems with continuous and/or discrete energy spectrum
| Authors | Dominik Janzing |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0407144 |
| URL | https://arxiv.org/abs/quant-ph/0407144 |
| DOI | 10.1063/1.2142839 |
Abstract
Every completely positive map G that commutes which the Hamiltonian time evolution is an integral or sum over (densely defined) CP-maps G_\sigma where \sigma is the energy that is transferred to or taken from the environment. If the spectrum is non-degenerated each G_\sigma is a dephasing channel followed by an energy shift. The dephasing is given by the Hadamard product of the density operator with a (formally defined) positive operator. The Kraus operator of the energy shift is a partial isometry which defines a translation on R with respect to a non-translation-invariant measure. As an example, I calculate this decomposition explicitly for the rotation invariant gaussian channel on a single mode. I address the question under what conditions a covariant channel destroys superpositions between mutually orthogonal states on the same orbit. For channels which allow mutually orthogonal output states on the same orbit, a lower bound on the quantum capacity is derived using the Fourier transform of the CP-map-valued measure (G_\sigma).
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"abstract": "Every completely positive map G that commutes which the Hamiltonian time\nevolution is an integral or sum over (densely defined) CP-maps G_\\sigma where\n\\sigma is the energy that is transferred to or taken from the environment. If\nthe spectrum is non-degenerated each G_\\sigma is a dephasing channel followed\nby an energy shift. The dephasing is given by the Hadamard product of the\ndensity operator with a (formally defined) positive operator. The Kraus\noperator of the energy shift is a partial isometry which defines a translation\non R with respect to a non-translation-invariant measure.\n As an example, I calculate this decomposition explicitly for the rotation\ninvariant gaussian channel on a single mode.\n I address the question under what conditions a covariant channel destroys\nsuperpositions between mutually orthogonal states on the same orbit. For\nchannels which allow mutually orthogonal output states on the same orbit, a\nlower bound on the quantum capacity is derived using the Fourier transform of\nthe CP-map-valued measure (G_\\sigma).",
"arxiv_id": "quant-ph/0407144",
"authors": [
"Dominik Janzing"
],
"categories": [
"quant-ph"
],
"doi": "10.1063/1.2142839",
"title": "Decomposition of time-covariant operations on quantum systems with continuous and/or discrete energy spectrum",
"url": "https://arxiv.org/abs/quant-ph/0407144"
},
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