dorsal/arxiv
View SchemaPermanents in linear optical networks
| Authors | Stefan Scheel |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0406127 |
| URL | https://arxiv.org/abs/quant-ph/0406127 |
| Journal | results are contained in Acta Physica Slovaca 58, 675 (2008) and in Chap.28 of Beth/Leuchs (eds.) 'Quantum Information Processing' (Wiley-VCH, Weinheim, 2005) |
Abstract
We develop an abstract look at linear optical networks from the viewpoint of combinatorics and permanents. In particular we show that calculation of matrix elements of unitarily transformed photonic multi-mode states is intimately linked to the computation of permanents. An implication of this remarkable fact is that all calculations that are based on evaluating matrix elements are generically computationally hard. Moreover, quantum mechanics provides simpler derivations of certain matrix analysis results which we exemplify by showing that the permanent of any unitary matrix takes its values across the unit disk in the complex plane.
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"abstract": "We develop an abstract look at linear optical networks from the viewpoint of\ncombinatorics and permanents. In particular we show that calculation of matrix\nelements of unitarily transformed photonic multi-mode states is intimately\nlinked to the computation of permanents. An implication of this remarkable fact\nis that all calculations that are based on evaluating matrix elements are\ngenerically computationally hard. Moreover, quantum mechanics provides simpler\nderivations of certain matrix analysis results which we exemplify by showing\nthat the permanent of any unitary matrix takes its values across the unit disk\nin the complex plane.",
"arxiv_id": "quant-ph/0406127",
"authors": [
"Stefan Scheel"
],
"categories": [
"quant-ph"
],
"journal_ref": "results are contained in Acta Physica Slovaca 58, 675 (2008) and\n in Chap.28 of Beth/Leuchs (eds.) \u0027Quantum Information Processing\u0027 (Wiley-VCH,\n Weinheim, 2005)",
"title": "Permanents in linear optical networks",
"url": "https://arxiv.org/abs/quant-ph/0406127"
},
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