Abstract

We consider a quantum mechanical state initially in a subspace $P$ of the full Hilbert space of the system and subjected to a sequence of appropriately spaced short-duration pulses. In between the pulses, the evolution of the system is governed by its Hamiltonian. The pulse adds a phase $\pi$ to the vectors in the subspace $P$. We construct a sequence of $N$ pulses within a finite time interval $T$ such that the probability of finding the system outside $P$ at $T$ can be made as small as $2^- (łog_2 N)^2$, for large $N$.

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