If we consider an efficient measurement performed on a system in a pure state. How would we use feedback (by applying to the system a unitary operator that depends upon the measurement result), to prepare the system in the same final state for every outcome of the measurement (this can be done for any efficient measurement).(adsbygoogle = window.adsbygoogle || []).push({});

So I think the idea is that say we start with a pure state $$\rho = | \psi \rangle \langle \psi|$$ and some desired final state after measurement $$\tilde{\rho}_n = \frac{A_n \rho A_n^{\dagger}}{p_n} = \frac{A_n | \psi \rangle \langle \psi | A_n ^{\dagger}}{p_n},$$ then we seek a unitary operator $$U_m$$ such that if $$m \neq n$$ then $$U_m A_m = A_n$$ thus resulting in $$\tilde{\rho}_m = \frac{U_mA_m | \psi \rangle \langle \psi | A_m^{\dagger}U^{\dagger}}{p_m} = \frac{A_n | \psi \rangle \langle \psi | A_n^{\dagger}}{p_n} = \tilde{\rho}_n.$$ I'm having difficulty thinking of how we could define this unitary operator $$U_m$$?

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# A Using feedback in quantum measurements

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