dorsal/arxiv
View SchemaReconstruction of superoperators from incomplete measurements
| Authors | Mario Ziman, Martin Plesch, Vladimir Buzek |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0406088 |
| URL | https://arxiv.org/abs/quant-ph/0406088 |
| DOI | 10.1007/s10701-005-9009-9 |
| Journal | Found Phys (2006) 36: 127 |
Abstract
We present strategies how to reconstruct (estimate) properties of a quantum channel described by the map E based on incomplete measurements. In a particular case of a qubit channel a complete reconstruction of the map E can be performed via complete tomography of four output states E[rho_j ] that originate from a set of four linearly independent test states j (j = 1, 2, 3, 4) at the input of the channel. We study the situation when less than four linearly independent states are transmitted via the channel and measured at the output. We present strategies how to reconstruct the channel when just one, two or three states are transmitted via the channel. In particular, we show that if just one state is transmitted via the channel then the best reconstruction can be achieved when this state is a total mixture described by the density operator rho = I/2. To improve the reconstruction procedure one has to send via the channel more states. The best strategy is to complement the total mixture with pure states that are mutually orthogonal in the sense of the Bloch-sphere representation. We show that unitary transformations (channels) can be uniquely reconstructed (determined) based on the information of how three properly chosen input states are transformed under the action of the channel.
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"abstract": "We present strategies how to reconstruct (estimate) properties of a quantum\nchannel described by the map E based on incomplete measurements. In a\nparticular case of a qubit channel a complete reconstruction of the map E can\nbe performed via complete tomography of four output states E[rho_j ] that\noriginate from a set of four linearly independent test states j (j = 1, 2, 3,\n4) at the input of the channel. We study the situation when less than four\nlinearly independent states are transmitted via the channel and measured at the\noutput. We present strategies how to reconstruct the channel when just one, two\nor three states are transmitted via the channel. In particular, we show that if\njust one state is transmitted via the channel then the best reconstruction can\nbe achieved when this state is a total mixture described by the density\noperator rho = I/2. To improve the reconstruction procedure one has to send via\nthe channel more states. The best strategy is to complement the total mixture\nwith pure states that are mutually orthogonal in the sense of the Bloch-sphere\nrepresentation. We show that unitary transformations (channels) can be uniquely\nreconstructed (determined) based on the information of how three properly\nchosen input states are transformed under the action of the channel.",
"arxiv_id": "quant-ph/0406088",
"authors": [
"Mario Ziman",
"Martin Plesch",
"Vladimir Buzek"
],
"categories": [
"quant-ph"
],
"doi": "10.1007/s10701-005-9009-9",
"journal_ref": "Found Phys (2006) 36: 127",
"title": "Reconstruction of superoperators from incomplete measurements",
"url": "https://arxiv.org/abs/quant-ph/0406088"
},
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