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We consider the existence in arbitrary finite dimensions d of a POVM comprised of d rank-one operators all of whose operator inner products are equal. Such a set is called a “symmetric, informationally complete” POVM (SIC-POVM) and is equivalent to a set of d equiangular lines in C . SIC-POVMs are relevant for quantum state tomography, quantum cryptography,(More)
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(More)
Electron energy-loss near-edge structure (ELNES) is a technique that can be used to measure the electronic structure (i.e. bonding) in materials with subnanometre spatial resolution. This review covers the theoretical principles behind the technique, the experimental procedures necessary to acquire good ELNES spectra, including potential artefacts, and(More)
Five yeast strains were isolated by enrichment culture on the basis of their ability to grow on mandelate and two of these strains were identified as Rhodotorula glutinis. In addition, a range of yeasts from culture collections was screened for growth on mandelate. The results suggest that mandelate utilization is a widespread but not universal(More)
A unitary design is a collection of unitary matrices that approximate the entire unitary group, much like a spherical design approximates the entire unit sphere. In this paper, we use irreducible representations of the unitary group to find a general lower bound on the size of a unitary t-design in U(d), for any d and t. We also introduce the notion of a(More)