0 v 1 1 1 D ec 2 00 6 Loss - Induced Limits to NOON - State Phase Measurement Precision ∗

The presence of loss limits the precision of an approach to phase measurement using NOON states. A calculation using a simple beam-splitter model of loss shows that, for all nonzero values L of the loss, phase measurement precision degrades with increasing number N of entangled photons for N sufficiently large. For L above a critical value of approximately 0.785, phase measurement precision degrades with increasing N for all values of N . For L near zero, phase measurement precision improves with increasing N down to a limiting precision of approximately 1.018L radians, attained at N approximately equal to 2.218/L, and degrades as N increases beyond this value. Phase measurement precision with multiple measurements and a fixed total number of photons NT is optimized, for L near zero, by using approximately 1.279/L entangled photons in each measurement, yielding a precision of approximately 1.340 √ L/NT radians. 1 NOON States and the Heisenberg Limit The use of NOON states has been proposed as a means of performing phase measurements with a precision δφmin at the Heisenberg limit. In this limit, δφmin scales as δφmin ∼ 1/N, (1) ∗This work was sponsored by the Air Force under Air Force Contract FA8721-05-C-0002. Opinions, interpretations, conclusions, and recommendations are those of the authors and are not necessarily endorsed by the U.S. Government.