Thursday, July 11, 2013

1307.2630 (Shengshi Pang et al.)

Amplification limit of weak measurement    [PDF]

Shengshi Pang, Todd A. Brun, Shengjun Wu, Zeng-Bing Chen
In this work, we solve the open problem of the amplification limit for a weak measurement with post-selection. The pre- and post-selected states of the system and the initial probe state are allowed to be arbitrary. We derive that the maximal output of a weak measurement is the solution of an eigenvalue equation, and reveal a remarkable property that the maximal output is essentially independent of both the observable on the system and the interaction strength, but only dependent on the dimension of the system and the initial state of the probe. As an example, we completely solve the case of dimension two, which is of particular interest for quantum information. We generalize our result to the case where the initial system and probe states are mixed states, and the post-selection is a POVM. Finally, we discuss the application of our result to designing weak measurement experiments.
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