We analyze the ultimate bounds on the phase sensitivity of an interferometer, given the constraint that the state input to the interferometer's initial 50:50 beamsplitter B is a product state of the two input modes. Requiring a product state is a natural restriction: if one were allowed to input an arbitrary, entangled two-mode state ∣Ξ⟩ to the beamsplitter, one could generally just as easily input the state B∣Ξ⟩ directly into the two modes after the beamsplitter, thus rendering the beamsplitter unnecessary. We find optimal states for a fixed photon number and for a fixed mean photon number.
@article{arxiv.1406.3274,
title = {Optimal Quantum-Enhanced Interferometry},
author = {Matthias D. Lang and Carlton M. Caves},
journal= {arXiv preprint arXiv:1406.3274},
year = {2014}
}