We derive the optimal -photon two-mode input state for obtaining an estimate of the phase difference between two arms of an interferometer. For an optimal measurement [B. C. Sanders and G. J. Milburn, Phys. Rev. Lett. 75, 2944 (1995)], it yields a variance , compared to or for states considered by previous authors. Such a measurement cannot be realized by counting photons in the interferometer outputs. However, we introduce an adaptive measurement scheme that can be thus realized, and show that it yields a variance in very close to that from an optimal measurement.
- Received 19 June 2000
- Published in the issue dated 11 December 2000
© 2000 The American Physical Society