A Quantum Anti-Zeno Paradox

Abstract

We establish an exact differential equation for the operator describing time-dependent measurements continuous in time and obtain a series solution. Suppose the projection operator $E(t)=U(t)E{U}^{†}(t)$ is measured continuously from t = 0 to T, where E is a projector leaving the initial state unchanged and U(t) a unitary operator obeying U(0) = 1 and some smoothness conditions in t. We prove that the probability of always finding E(t) = 1 from t = 0 to T is unity. If $U(t)\ne 1$, the watched kettle is sure to `boil'.

10 pages,latex

References in corpus (2)

• Berry phase from a quantum Zeno effect
• Quantum Zeno effect in the decay onto an unstable level

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