dorsal/arxiv
View SchemaMinimal Informationally Complete Measurements for Pure States
| Authors | Steven T. Flammia, Andrew Silberfarb, Carlton M. Caves |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0404137 |
| URL | https://arxiv.org/abs/quant-ph/0404137 |
| DOI | 10.1007/s10701-005-8658-z |
| Journal | Foundations of Physics, Volume 35, Issue 12, Dec 2005, pp. 1985 - 2006 |
Abstract
We consider measurements, described by a positive-operator-valued measure (POVM), whose outcome probabilities determine an arbitrary pure state of a D-dimensional quantum system. We call such a measurement a pure-state informationally complete (PSI-complete) POVM. We show that a measurement with 2D-1 outcomes cannot be PSI-complete, and then we construct a POVM with 2D outcomes that suffices, thus showing that a minimal PSI-complete POVM has 2D outcomes. We also consider PSI-complete POVMs that have only rank-one POVM elements and construct an example with 3D-2 outcomes, which is a generalization of the tetrahedral measurement for a qubit. The question of the minimal number of elements in a rank-one PSI-complete POVM is left open.
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"abstract": "We consider measurements, described by a positive-operator-valued measure\n(POVM), whose outcome probabilities determine an arbitrary pure state of a\nD-dimensional quantum system. We call such a measurement a pure-state\ninformationally complete (PSI-complete) POVM. We show that a measurement with\n2D-1 outcomes cannot be PSI-complete, and then we construct a POVM with 2D\noutcomes that suffices, thus showing that a minimal PSI-complete POVM has 2D\noutcomes. We also consider PSI-complete POVMs that have only rank-one POVM\nelements and construct an example with 3D-2 outcomes, which is a generalization\nof the tetrahedral measurement for a qubit. The question of the minimal number\nof elements in a rank-one PSI-complete POVM is left open.",
"arxiv_id": "quant-ph/0404137",
"authors": [
"Steven T. Flammia",
"Andrew Silberfarb",
"Carlton M. Caves"
],
"categories": [
"quant-ph"
],
"doi": "10.1007/s10701-005-8658-z",
"journal_ref": "Foundations of Physics, Volume 35, Issue 12, Dec 2005, pp. 1985 -\n 2006",
"title": "Minimal Informationally Complete Measurements for Pure States",
"url": "https://arxiv.org/abs/quant-ph/0404137"
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