is given by $r=a_2$.

![An example of a basic measurement on two systems, each with $x,a \in \{0,1\}$. []{data-label="fig:basic_measurement"}](basic_measurement2.eps)

In general, it is reasonable to require that measurements of this form are in the set of allowed measurements in an operational model. In fact, as we can also choose such basic measurements at random, it is also reasonable to require that convex combinations of basic measurements (defined in an obvious way) are allowed. Note that for a single system, each basic measurement corresponds to a fiducial measurement, possibly with relabelled outputs.

All valid measurements on single or bipartite systems in box world are convex combinations of basic measurements. \[wiringtheorem\]

This means that any measurement on a single or bipartite system can be implemented by a probabilistic protocol involving only fiducial measurements. Especially given Corollary \[noenteffect\], it would be natural to assume that Theorem \[wiringtheorem\] generalises to multi-partite systems in box world, and indeed this was hypothesized in Ref. [@barrett]. However, things are not so simple.

For tri-partite systems, there are measurements which do not reduce to a convex combination of basic measurements.\[3systemtheorem\]

Section \[counterexample\] illustrates this with a specific example.

Finally, there is at least some limitation on the power 