= N-box pre- and post-selection paradox
{c}
{title2=$D=N^2-N+1$}
For a uniform prestate in $N+1$ dimensions and poststate proportional to $\sum_{i=1}^N|i\rangle-(N-1)|N+1\rangle$, each binary question $P_i$ versus $I-P_i$ has conditional probability one for $i\leq N$. A fully resolved <quantum measurement> instead assigns $1/D$ to each of the first $N$ outcomes and $(N-1)^2/D$ to the last. The <context dependence of pre- and post-selected measurements> explains why these alternative certainties do not imply simultaneous properties.
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