Phase fromQfunction via linear amplification

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Abstract
We relate the phase distribution of a quantum state obtained by integrating its corresponding Q function over radius (1) to a specific measurement scheme using a linear amplifier and (2) to a particular phase operator. A simple relation between the P distribution of the amplified macroscopic state and the Q function of the initial unamplified microscopic state allows us to prove the identity of the phase distributions obtained by integrating the corresponding distributions.