  Given a quantum system $S$ entangled with another system $I$, the
entanglement testing problem arises, prompting the identification of the system
$S$ within a set of $m \ge 2$ identical systems. This scenario serves as a
model for the measurement task encountered in quantum ranging and
entanglement-assisted communication [Phys. Rev. Lett. 126, 240501, (2021)]. In
this context, the optimal measurement approach typically involves joint
measurements on all $m+1$ systems. However, we demonstrate that this is not the
case when the subsystems containing system $S$ are subjected to
entanglement-breaking noise. Our approach utilizes the recently developed
measurement technique of correlation-to-displacement conversion. We present a
structured design for the entanglement testing measurement, implementable with
local operations and classical communications (LOCC) on the $m+1$ systems.
Furthermore, we prove that this measurement approach achieves optimality in
terms of error probability asymptotically under noisy conditions. When applied
to quantum illumination, our measurement design enables optimal ranging in
scenarios with low signal brightness and high levels of noise. Similarly, when
applied to entanglement-assisted classical communication, the measurement
design leads to a significant relative advantage in communication rates,
particularly in scenarios with low signal brightness.
