Abstract
Using a conservation law obeyed by the degenerate parametric amplifier, we find a bound to the accuracy that can be obtained by using the signal mode to measure a phase shift. In particular, we show that there is a limit, which depends only on the initial state of the pump and signal modes, on how sharp the phase distribution of the signal mode can be. If the pump mode is initially in a coherent state and the signal mode is in the vacuum state, the phase distribution of the signal mode can be sharper than that of the initial state of the pump mode by at most a factor of two.
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