Limits of quantum-enhanced metrology under noise

4 problems

• Optimal scaling of atomic-clock stability with atom number under laser noise

  Partially resolved

  A clock steers a laser using N atoms, but the laser itself jitters, which limits how long atoms can be probed. The best possible improvement from entangling the atoms, given this jitter, is not known.

• Precision scaling under spatially correlated and non-Markovian dephasing

  Open

  Real noise often hits all atoms together or has memory in time. How the best achievable precision then scales with particle number and time is known only in special cases.

• Can entanglement improve a clock already at the stability frontier?

  Open

  Squeezed atom states (correlated states with reduced noise in one quantity) have beaten the standard limit in clocks, but only in setups that were not the most stable clocks available. The question is whether entanglement can improve the very best clocks in absolute terms.

• Heisenberg scaling with error correction under imperfect control

  Partially resolved

  Quantum error correction can restore the ideal 1/N gain when the signal and the noise act differently on the sensor. It is open in general whether this still works when the correcting operations are themselves noisy.