dorsal/arxiv
View SchemaAn algorithm to perform POVMs through Neumark theorem: application to the discrimination of non-orthogonal pure quantum states
| Authors | Wilson R. M. Rabelo, Alexandre G. Rodrigues, Reinaldo O. Vianna |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0509191 |
| URL | https://arxiv.org/abs/quant-ph/0509191 |
| DOI | 10.1142/S0129183106008911 |
| Journal | International Journal of Modern Physics C, 17, 1203-1218 (2006) |
Abstract
We consider a protocol to perform the optimal quantum state discrimination of $N$ linearly independent non-orthogonal pure quantum states and present a computational code. Through the extension of the original Hilbert space, it is possible to perform an unitary operation yielding a final configuration, which gives the best discrimination without ambiguity by means of von Neumann measurements. Our goal is to introduce a detailed general mathematical procedure to realize this task by means of semidefinite programming and norm minimization. The former is used to fix which is the best detection probability amplitude for each state of the ensemble. The latter determines the matrix which leads the states to the final configuration. In a final step, we decompose the unitary transformation in a sequence of two-level rotation matrices.
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"abstract": "We consider a protocol to perform the optimal quantum state discrimination of\n $N$ linearly independent non-orthogonal pure quantum states and present a\ncomputational code. Through the extension of the original Hilbert space, it is\npossible to perform an unitary operation yielding a final configuration, which\ngives the best discrimination without ambiguity by means of von Neumann\nmeasurements. Our goal is to introduce a detailed general mathematical\nprocedure to realize this task by means of semidefinite programming and norm\nminimization.\n The former is used to fix which is the best detection probability amplitude\nfor each state of the ensemble. The latter determines the matrix which leads\nthe states to the final configuration. In a final step, we decompose the\nunitary transformation in a sequence of two-level rotation matrices.",
"arxiv_id": "quant-ph/0509191",
"authors": [
"Wilson R. M. Rabelo",
"Alexandre G. Rodrigues",
"Reinaldo O. Vianna"
],
"categories": [
"quant-ph"
],
"doi": "10.1142/S0129183106008911",
"journal_ref": "International Journal of Modern Physics C, 17, 1203-1218 (2006)",
"title": "An algorithm to perform POVMs through Neumark theorem: application to the discrimination of non-orthogonal pure quantum states",
"url": "https://arxiv.org/abs/quant-ph/0509191"
},
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