Tight informationally complete quantum measurements

Details Tight informationally complete quantum measurements Tight informationally complete quantum measurements

2006-04-07

arxiv.org/abs/quant-ph/0604049v6

J. Phys. A 39, 13507 (2006)

Physics

Quantum Physics

20 pages. Final version

Scientific paper

10.1088/0305-4470/39/43/009

We introduce a class of informationally complete positive-operator-valued measures which are, in analogy with a tight frame, "as close as possible" to orthonormal bases for the space of quantum states. These measures are distinguished by an exceptionally simple state-reconstruction formula which allows "painless" quantum state tomography. Complete sets of mutually unbiased bases and symmetric informationally complete positive-operator-valued measures are both members of this class, the latter being the unique minimal rank-one members. Recast as ensembles of pure quantum states, the rank-one members are in fact equivalent to weighted 2-designs in complex projective space. These measures are shown to be optimal for quantum cloning and linear quantum state tomography.

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