期刊
FOUNDATIONS OF PHYSICS
卷 35, 期 12, 页码 1985-2006出版社
SPRINGER
DOI: 10.1007/s10701-005-8658-z
关键词
quantum state tomography; informationally complete measurement; positive operator-valued measure
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 (PS I-complete) POVM. We show that a measurement with 2D-1 outcomes cannot be PS I-complete, and then we construct a POVM with 2D outcomes that suffices, thus showing that a minimal PS I-complete POVM has 2D outcomes. We also consider PS I-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 PS I-complete POVM is left open.
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