  By using a systematic optimization approach we determine quantum states of
light with definite photon number leading to the best possible precision in
optical two mode interferometry. Our treatment takes into account the
experimentally relevant situation of photon losses. Our results thus reveal the
benchmark for precision in optical interferometry. Although this boundary is
generally worse than the Heisenberg limit, we show that the obtained precision
beats the standard quantum limit thus leading to a significant improvement
compared to classical interferometers. We furthermore discuss alternative
states and strategies to the optimized states which are easier to generate at
the cost of only slightly lower precision.
