30 August 2017 Some examples of sum uncertainty relations for compact classical Lie algebra
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Abstract
We formulate the sum uncertainty relations for compact classical Lie algebras of the type su (n), so (2n), so (2n + 1) and sp (n). Then we present resulting uncertainty relations explicitly for the su (2) ; su (3) and su (4) cases. We numerically verified our bound by choosing a large number of random vectors within an irrep of each of these algebras. We verify the bounds for several irreps. We discuss what type of states saturate su (n) bound for n = 2; 3 and 4, and compare these states with states that saturate more familiar products uncertainty relations.
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Namrata Shukla, Hubert de Guise, Lorenzo Maccone, Barry C. Sanders, "Some examples of sum uncertainty relations for compact classical Lie algebra", Proc. SPIE 10409, Quantum Communications and Quantum Imaging XV, 104090S (30 August 2017); doi: 10.1117/12.2275349; https://doi.org/10.1117/12.2275349
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