Fisher-Symmetric Informationally Complete Measurements for Pure States

Publication Type:
Journal Article
Physical Review Letters, 2016, 116 (18)
Issue Date:
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© 2016 American Physical Society. We introduce a new kind of quantum measurement that is defined to be symmetric in the sense of uniform Fisher information across a set of parameters that uniquely represent pure quantum states in the neighborhood of a fiducial pure state. The measurement is locally informationally complete - i.e., it uniquely determines these parameters, as opposed to distinguishing two arbitrary quantum states - and it is maximal in the sense of a multiparameter quantum Cramér-Rao bound. For a d-dimensional quantum system, requiring only local informational completeness allows us to reduce the number of outcomes of the measurement from a minimum close to but below 4d-3, for the usual notion of global pure-state informational completeness, to 2d-1.
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