Tomographic and Lie algebraic significance of generalized symmetric informationally complete measurements
arXiv:1408.0560 · doi:10.1103/PhysRevA.90.032309
Abstract
Generalized symmetric informationally complete (SIC) measurements are SIC measurements that are not necessarily rank one. They are interesting originally because of their connection with rank-one SICs. Here we reveal several merits of generalized SICs in connection with quantum state tomography and Lie algebra that are interesting in their own right. These properties uniquely characterize generalized SICs among minimal IC measurements although, on the face of it, they bear little resemblance to the original definition. In particular, we show that in quantum state tomography generalized SICs are optimal among minimal IC measurements with given average purity of measurement outcomes. Besides its significance to the current study, this result may help understand tomographic efficiencies of minimal IC measurements under the influence of noise. When minimal IC measurements are taken as bases for the Lie algebra of the unitary group, generalized SICs are uniquely characterized by the antisymmetry of the associated structure constants.
arXiv comment6.2 pages, comments and suggestions welcome
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- Quantum Conical Designs
- Shadow tomography on general measurement frames
- Mutually unbiased bases as minimal Clifford covariant 2-designs
- Construction of general symmetric-informationally-complete-positive-operator-valued measures by using a complete orthogonal basis
- Quantum Measurements in the Light of Quantum State Estimation
- Completeness Stability of Quantum Measurements