  Despite their importance in quantum theory, joint quantum measurements remain
poorly understood. An intriguing conceptual and practical question is whether
joint quantum measurements on separated systems can be performed without
bringing them together. Remarkably, by using shared entanglement, this can be
achieved perfectly when disregarding the post-measurement state. However,
existing localization protocols typically require unbounded entanglement. In
this work, we address the fundamental question: "Which joint measurements can
be localized with a finite amount of entanglement?" We develop finite-resource
versions of teleportation-based schemes and analytically classify all two-qubit
measurements that can be localized in the first steps of these hierarchies.
These include several measurements with exceptional properties and symmetries,
such as the Bell state measurement and the elegant joint measurement. This
leads us to propose a systematic classification of joint measurements based on
entanglement cost, which we argue directly connects to the complexity of
implementing those measurements. We illustrate how to numerically explore
higher levels and construct generalizations to higher dimensions and
multipartite settings.
