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Minimal Informationally Complete Measurements for Pure States
Steven T. Flammia, Andrew Silberfarb, Carlton M. Caves
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.
- oai_identifier:
- oai:arXiv.org:quant-ph/0404137
- categories:
- quant-ph
- comments:
- 2 figures, submitted for the Asher Peres festschrift
- doi:
- 10.1007/s10701-005-8658-z
- arxiv_id:
- quant-ph/0404137
- journal_ref:
- Foundations of Physics, Volume 35, Issue 12, Dec 2005, pp. 1985 -
2006
- created:
- 2004-04-23
Full article ▸
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