Tight informationally complete quantum measurements

Abstract

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.

20 pages. Final version

Cited by in corpus (5)

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• Choice of Measurement Sets in Qubit Tomography
• Optimizing quantum process tomography with unitary 2-designs
• Weighted complex projective 2-designs from bases: optimal state determination by orthogonal measurements
• Optimal quantum tomography for states, measurements, and transformations