On construction of finite averaging sets for $SL(2, \mathbb{C})$ via its Cartan decomposition
Marcin Markiewicz,
Janusz Przewocki
Abstract:Averaging physical quantities over Lie groups appears in many contexts across the rapidly developing branches of physics like quantum information science or quantum optics. Such an averaging process can be always represented as averaging with respect to a finite number of elements of the group, called a finite averaging set.In the previous research such sets, known as t-designs, were constructed only for the case of averaging over unitary groups (hence the name unitary t-designs). In this work we investigate t… Show more
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