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arXiv · 1507.06904

Fisher-symmetric informationally complete measurements for pure states

Nan Li·Christopher Ferrie·Jonathan A. Gross·Amir Kalev·Carlton M. Caves
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Abstract

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 injectively 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 multi-parameter quantum Cramer-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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Nan Li, Christopher Ferrie, Jonathan A. Gross, Amir Kalev, Carlton M. Caves. 2016-02-16. Fisher-symmetric informationally complete measurements for pure states. https://doi.org/10.1103/physrevlett.116.180402

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