Quantum Information measures for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si103.svg" display="inline" id="d1e1032"> <mml:mi>α</mml:mi> </mml:math> – <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si104.svg" display="inline" id="d1e1037"> <mml:msub> <mml:mrow> <mml:mi mathvariant="script">T</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>3</mml:mn> </mml:mrow> </mml:msub> </mml:math> Lattice quantum dots in magnetic fields