Thursday, July 18, 2013

1307.4524 (Antonio Di Lorenzo)

Weak values maximizing the output of weak measurements    [PDF]

Antonio Di Lorenzo
In a weak measurement, the average output $\langle p\rangle$ of a probe that measures an observable $\Hat{A}$ of a quantum system undergoing both a preparation in a state $\rho_i$ and a postselection in a state $E_f$ is, to a good approximation, a function of the weak value $A_w=\Tr[E_f\Hat{A}\rho_i]/\Tr[E_f\rho_i]$, a complex number. For a fixed coupling, when the overlap $\Tr[E_f\rho_i]$ is very small, $A_w$ diverges, but $\langle p\rangle$ stays finite, often tending to zero for symmetry reasons. This paper answers the question: which are the extremal values of the output as a function of the weak value? We derive equations for the optimal values of $A_w$, and provide the solutions. The results are independent of the dimensionality of the system.
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