Quantum Communications and Quantum Imaging

Some examples of sum uncertainty relations for compact classical Lie algebra

Namrata Shukla, Hubert de Guise, Lorenzo Maccone, Barry C. Sanders

Published Aug 30, 2017• 0 citations

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.

DOI: 10.1117/12.2275349

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