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.

Date Published: 30 August 2017
PDF: 7 pages
Proc. SPIE 10409, Quantum Communications and Quantum Imaging XV, 104090S (30 August 2017); doi: 10.1117/12.2275349

Published in SPIE Proceedings Vol. 10409:
Quantum Communications and Quantum Imaging XV
Ronald E. Meyers; Yanhua Shih; Keith S. Deacon, Editor(s)