dorsal/arxiv
View SchemaMultiple Qubits as Symplectic Polar Spaces of Order Two
| Authors | Metod Saniga, Michel Planat |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0612179 |
| URL | https://arxiv.org/abs/quant-ph/0612179 |
| Journal | Advanced Studies in Theoretical Physics 1 (2007) 1 - 4 |
Abstract
It is surmised that the algebra of the Pauli operators on the Hilbert space of N-qubits is embodied in the geometry of the symplectic polar space of rank N and order two, W_{2N - 1}(2). The operators (discarding the identity) answer to the points of W_{2N - 1}(2), their partitionings into maximally commuting subsets correspond to spreads of the space, a maximally commuting subset has its representative in a maximal totally isotropic subspace of W_{2N - 1}(2) and, finally, "commuting" translates into "collinear" (or "perpendicular").
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"abstract": "It is surmised that the algebra of the Pauli operators on the Hilbert space\nof N-qubits is embodied in the geometry of the symplectic polar space of rank N\nand order two, W_{2N - 1}(2). The operators (discarding the identity) answer to\nthe points of W_{2N - 1}(2), their partitionings into maximally commuting\nsubsets correspond to spreads of the space, a maximally commuting subset has\nits representative in a maximal totally isotropic subspace of W_{2N - 1}(2)\nand, finally, \"commuting\" translates into \"collinear\" (or \"perpendicular\").",
"arxiv_id": "quant-ph/0612179",
"authors": [
"Metod Saniga",
"Michel Planat"
],
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"quant-ph",
"math-ph",
"math.MP"
],
"journal_ref": "Advanced Studies in Theoretical Physics 1 (2007) 1 - 4",
"title": "Multiple Qubits as Symplectic Polar Spaces of Order Two",
"url": "https://arxiv.org/abs/quant-ph/0612179"
},
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