Abstract
Abstract Chapter 17 deals with the description of high-dimensional quantum systems and entanglement between them. We start with the generalized Bloch decomposition and present several useful options for the choice of operator bases, including the generalized Gell-Mann basis, the polarization-operator basis, and the Weyl-operator basis. We apply these bases for the example of isotropic two-qudit states and for the detection of bound entanglement for systems of two qutrits. We then turn to the problem of detecting entanglement in high-dimensional systems. For this purpose we review mutually unbiased bases and employ them for entanglement detection. We then discuss entanglement detection using entropic uncertainty relations, before we show how to obtain lower bounds on pure-state fidelities, on the entanglement of formation, and on the Schmidt number from measurement in pairs of mutually unbiased bases
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