Positive contraction
= Positive contraction
{title2=$0\leq M\leq I$}
A positive contraction is a <positive operator> whose <operator norm> is at most one. Its <spectrum> lies in $[0,1]$, so the <spectral theorem for normal operators> gives $M^2\leq M$. Positive contractions are the effects in a <POVM> and occur in the <pure-state gentle measurement bound>.