Some examples of sum uncertainty relations for compact classical Lie algebra

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

doi:10.1117/12.2275349

30 August 2017 Some examples of sum uncertainty relations for compact classical Lie algebra

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

Proceedings Volume 10409, Quantum Communications and Quantum Imaging XV; 104090S (2017) https://doi.org/10.1117/12.2275349
Event: SPIE Optical Engineering + Applications, 2017, San Diego, California, United States

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.

Citation Download Citation

Namrata Shukla, Hubert de Guise, Lorenzo Maccone, and 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); https://doi.org/10.1117/12.2275349

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