  We introduce a super-sensitive phase measurement technique that yields the
Heisenberg limit without using either a squeezed state or a many-particle
entangled state. Instead, we use a many-particle separable quantum state to
probe the phase and we then retrieve the phase through single-particle
interference. The particles that physically probe the phase are never detected.
Our scheme involves no coincidence measurement or many-particle interference
and yet exhibits phase super-resolution. We also analyze in detail how the loss
of probing particles affects the measurement sensitivity and find that the loss
results in the generation of many-particle entanglement and the reduction of
measurement sensitivity. When the loss is maximum, the system produces a
many-particle Greenberger-Horne-Zeilinger (GHZ) state, and the phase
measurement becomes impossible due to very high phase uncertainty. In striking
contrast to the super-sensitive phase measurement techniques that use
entanglement involving two or more particles as a key resource, our method
shows that having many-particle entanglement can be counterproductive in
quantum metrology.
