Heisenberg scaling and resources
Correlated quantum probes can improve ideal phase sensitivity relative to independent probes.
$$\Delta\theta\propto N^{-1}$$
Physical intuition
Correlated quantum probes can improve ideal phase sensitivity relative to independent probes.
Deep dive: physical mechanism
For unitary phase encoding and suitable entangled probes, generator variance can scale quadratically with N, but realistic losses can remove the advantage.
What is measured experimentally?
Compare QFI of a GHZ state with N independent probes at fixed interrogation time.
Assumptions, noise and limitations
Heisenberg scaling is not a universal achievable bound in noisy sensors; count all resources.
Research and simulation exercise
Simulate phase sensitivity with GHZ probes under increasing dephasing.
Connect the ideas
Explore the chapter overview, learning path, and references.