of measurements in box world, even in the multi-partite case.

For any single or multi-partite system, all allowed measurements can be simulated using fiducial measurements and post-selection (i.e., the measurement is allowed to sometimes fail). \[postselecttheorem\]

Proofs
======

Some preliminary remarks will be useful. First, recall Theorem \[positivity\], which states that the entries of an effect ${\mathbf{R}}$ can be assumed non-negative. This is used throughout this section.

Now consider the arrays ${\mathbf{R}}_r$ corresponding to the outcomes of a basic measurement. Suppose that a basic measurement is carried out, with final outcome $r$, and that during its execution, the fiducial measurements ${\mathbf{x}}$ are performed, with outcomes ${\mathbf{a}}$. In this case, say that the triple $\{r,{\mathbf{a}},{\mathbf{x}}\}$ is realized. A basic measurement can be represented such that the component $R_r({\mathbf{a}}|{\mathbf{x}})$ is equal to 1 if and only if it is possible for $\{r,{\mathbf{a}},{\mathbf{x}}\}$ to be realized, else it is 0. From hereon we make this choice. For example, the bipartite measurement illustrated in Fig. \[fig:basic\_measurement\] is represented by $$\begin{aligned}
R_0(a_1 a_2| x_1 x_2) &=& \left( \begin{array}{c|c}  \begin{array}{cc} 1&0 \\ 0&0 \end{array}  &   \begin{array}{cc} 0&0 \\ 1&0  \end{array} \\
\hline  \begin{array}{cc} 0&0 \\ 0&0 \end{array}  &
\begin{array}{cc} 0&0 \\ 0&0 \end{array} \end{array} \right),
\label{r0example}\\
