Compressed sensing has demonstrated that a general signal
x∈Fn (
F∈{R,C}) can be estimated from few linear measurements with an error {proportional to} the best
k-term approximation error, a property known as instance optimality. In this paper, we investigate instance optimality in the context of phaseless measurements using the
ℓp-minimization decoder, where
p∈(0,1], for both real and complex cases. More specifically, we prove that
(2,1) and
(1,1)-instance optimality of order
k can be achieved with
m=O(klog(n/k)) phaseless measurements, paralleling results from linear measurements. These results imply that one can stably recover approximately
k-sparse signals from
m=O(klog(n/k)) phaseless measurements. Our approach leverages the phaseless bi-Lipschitz condition. Additionally, we present a non-uniform version of
(2,2)-instance optimality result in probability applicable to any fixed vector
x∈Fn. These findings reveal striking parallels between compressive phase retrieval and classical compressed sensing, enhancing our understanding of both phase retrieval and instance optimality.