dorsal/arxiv
View SchemaTomography of one and two qubit states and factorisation of the Wigner distribution in prime power dimensions
| Authors | Thomas Durt |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0604117 |
| URL | https://arxiv.org/abs/quant-ph/0604117 |
Abstract
We study different techniques that allow us to gain complete knowledge about an unknown quantum state, e.g. to perform full tomography of this state. We focus on two apparently simple cases, full tomography of one and two qubit systems. We analyze and compare those techniques according to two figures of merit. Our first criterion is the minimisation of the redundancy of the data acquired during the tomographic process. In the case of two-qubits tomography, we also analyze this process from the point of view of factorisability, so to say we analyze the possibility to realise the tomographic process through local operations and classical communications between local observers. This brings us naturally to study the possibility to factorize the (discrete) Wigner distribution of a composite system into the product of local Wigner distributions. The discrete Heisenberg-Weyl group is an essential ingredient of our approach. Possible extensions of our results to higher dimensions are discussed in the last section and in the conclusions.
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"abstract": "We study different techniques that allow us to gain complete knowledge about\nan unknown quantum state, e.g. to perform full tomography of this state. We\nfocus on two apparently simple cases, full tomography of one and two qubit\nsystems. We analyze and compare those techniques according to two figures of\nmerit. Our first criterion is the minimisation of the redundancy of the data\nacquired during the tomographic process. In the case of two-qubits tomography,\nwe also analyze this process from the point of view of factorisability, so to\nsay we analyze the possibility to realise the tomographic process through local\noperations and classical communications between local observers. This brings us\nnaturally to study the possibility to factorize the (discrete) Wigner\ndistribution of a composite system into the product of local Wigner\ndistributions. The discrete Heisenberg-Weyl group is an essential ingredient of\nour approach. Possible extensions of our results to higher dimensions are\ndiscussed in the last section and in the conclusions.",
"arxiv_id": "quant-ph/0604117",
"authors": [
"Thomas Durt"
],
"categories": [
"quant-ph"
],
"title": "Tomography of one and two qubit states and factorisation of the Wigner distribution in prime power dimensions",
"url": "https://arxiv.org/abs/quant-ph/0604117"
},
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