"Breathing pyrochlores" are a new class of material that contain sublattices of corner sharing tetrahedra, where the the sizes of the tetrahedra differ on the different sublattices. The recently synthesised Ba3Yb2Zn5O11 has been reported to be such a geometrically frustrated pyrochlore, in which the Yb ions adopt a pseudo-spin-1/2 ground state. The measured negative Curie-Weiss temperature indicates significant antiferromagnetic exchange couplings. However, no long range order has been observed to sub-Kelvin temperatures, and a proposed theoretical model predicts the emergence of a quantum spin ice state in breathing pyrochlores. We propose to investigate and characterise the magnetic ground state of this material using positive muons as local magnetic probes, utilising their sensitivity to long range order formation and the dynamics of the magnetic moments.