This article examines how digital systems designers distil the messiness and ambiguity of the world into concrete data that can be processed by computing systems. Using Karen Barad's agential realism as a guide, we explore how data is fundamentally entangled with the tools and theories of its measurement. We examine data-enabled artefacts acting as Baradian apparatuses: they do not exist independently of the phenomenon they seek to measure but rather collect and co-produce observations from within their entangled state: the phenomenon and the apparatus co-constitute one another. Connecting Barad's quantum view of indeterminacy to the prevailing HCI discourse on the opportunities and challenges of ambiguity, we suggest that the very act of trying to stabilise a conceptual interpretation of data within an artefact has the paradoxical effect of amplifying and shifting ambiguity in interaction. We illustrate these ideas through three case studies from our own practices of designing digital musical instruments (DMIs). DMIs necessarily encode symbolic and music-theoretical knowledge as part of their internal operation, even as conceptual knowledge is not their intended outcome. In each case, we explore the nature of the apparatus, what phenomena it co-produces, and where the ambiguity lies to suggest approaches for design using these abstract theoretical frameworks.