dorsal/arxiv
View SchemaOptimal unambiguous state discrimination of two density matrices: A second class of exact solutions
| Authors | Philippe Raynal, Norbert Lütkenhaus |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0702022 |
| URL | https://arxiv.org/abs/quant-ph/0702022 |
| DOI | 10.1103/PhysRevA.76.052322 |
| Journal | Phys. Rev. A Vol 76, 052322 (2007) |
Abstract
We consider the Unambiguous State Discrimination (USD) of two mixed quantum states. We study the rank and the spectrum of the elements of an optimal USD measurement. This naturally leads to a partial fourth reduction theorem. This theorem shows that either the failure probability equals its overall lower bound given in term of the fidelity or a two-dimensional subspace can be split off from the original Hilbert space. We then use this partial reduction theorem to derive the optimal solution for any two equally probable Geometrically Uniform (GU) states $\rho_0$ and $\rho_1=U\rho_0 U^\dagger$, $U^2={\openone}$, in a four-dimensional Hilbert space. This represents a second class of analytical solutions for USD problems that cannot be reduced to some pure state cases. We apply our result to answer two questions that are relevant in implementations of the Bennett and Brassard 1984 quantum key distribution protocol using weak coherent states.
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"abstract": "We consider the Unambiguous State Discrimination (USD) of two mixed quantum\nstates. We study the rank and the spectrum of the elements of an optimal USD\nmeasurement. This naturally leads to a partial fourth reduction theorem. This\ntheorem shows that either the failure probability equals its overall lower\nbound given in term of the fidelity or a two-dimensional subspace can be split\noff from the original Hilbert space. We then use this partial reduction theorem\nto derive the optimal solution for any two equally probable Geometrically\nUniform (GU) states $\\rho_0$ and $\\rho_1=U\\rho_0 U^\\dagger$, $U^2={\\openone}$,\nin a four-dimensional Hilbert space. This represents a second class of\nanalytical solutions for USD problems that cannot be reduced to some pure state\ncases. We apply our result to answer two questions that are relevant in\nimplementations of the Bennett and Brassard 1984 quantum key distribution\nprotocol using weak coherent states.",
"arxiv_id": "quant-ph/0702022",
"authors": [
"Philippe Raynal",
"Norbert L\u00fctkenhaus"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.76.052322",
"journal_ref": "Phys. Rev. A Vol 76, 052322 (2007)",
"title": "Optimal unambiguous state discrimination of two density matrices: A second class of exact solutions",
"url": "https://arxiv.org/abs/quant-ph/0702022"
},
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