Analytical and Phase Space Description of “Near” States

We investigate a conditional quantum state preparation process for a generalized form of the ‘near states’ in various representations. We derive transformation rules for the analytical representation of pure states. Additionally, we obtain transformation rules for both the Glauber-Sudarshan and Wigner representations of states. The latter is particularly convenient for calculating the output state when dealing with mixed states. Furthermore, we demonstrate that small thermal noises can effectively increase success probability without compromising the nonclassical properties of the output state.