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In the classical phase retrieval problem in the Paley-Wiener class $PW_L$ for$L>0$, i.e. to recover $f\in PW_L$ from $|f|$, Akutowicz, Walther, andHofstetter independently showed that all such solutions can be obtained byflipping an arbitrary set of complex zeros across the real line. This operationis called zero-flipping and we denote by $\mathfrak{F}_a f$ the resultingfunction. The operator $\mathfrak{F}_a$ is defined even if $a$ is not a genuinezero of $f$, that is if we make an error on the location of the zero. Our maingoal is to investigate the effect of $\mathfrak{F}_a$. We show that$\mathfrak{F}_af$ is no longer bandlimited but is still wide-banded. We theninvestigate the effect of $\mathfrak{F}_a$ on the stability of phase retrievalby estimating the quantity $\inf_{|c|=1}\|cf-\mathfrak{F}_af\|_2$. We show thatthis quantity is in general not well-suited to investigate stability, and so weintroduce the quantity $\inf_{|c|=1}\|c\mathfrak{F}_bf-\mathfrak{F}_af\|_2$. Weshow that this quantity is dominated by the distance between $a$ and $b$.

On the effect of zero-flipping on the stability of the phase retrieval problem in the Paley-Wiener class