 Quantum Zeno effect

Inhibition of a transition by increasingly frequent ideal projective measurements that check whether a quantum system remains in its initial quantum state. For a normalized vector $\psi$, a fixed Hamiltonian operator $H$ and the orthogonal projection $P=|\psi ⟩⟨\psi |$, the probability of passing every check at $N$ equally spaced times up to fixed time $T$ isFor a finite-dimensional Hilbert space, the quadratic short-time quantum survival probability implies ${\mathbb{P}}_N(T)\to 1$. This is an ideal limit with instantaneous measurements and unitary time evolution between them.