SU(2)-Equivariant Quantum Channels: Semiclassical Analysis

Abstract We study completely positive and trace-preserving equivariant maps between operators on irreducible representations of $${{\,\textrm{SU}\,}}(2)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mrow> <mml:mspace/> <mml:mtext>SU</mml:mtext> <mml:mspace/> </mml:mrow> <mml:mo>(</mml:mo> <mml:mn>2</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> . We find asymptotic approximations of channels in the limit of large output representation and we compute traces of functions of channel outputs. Our main tool is quantization using coherent states. We provide quantitative error bounds for various semiclassical formulas satisfied by quantizations of functions on the sphere.