A Quantum Anti-Zeno Paradox

Details A Quantum Anti-Zeno Paradox A Quantum Anti-Zeno Paradox

1999-09-17

arxiv.org/abs/quant-ph/9909056v1

Phys.Rev.Lett.84:4019-4022,2000

Physics

Quantum Physics

10 pages,latex

Scientific paper

10.1103/PhysRevLett.84.4019

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 $E(t) = U(t) E U^\dagger(t)$ 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 $U(t) \neq 1$, the watched kettle is sure to `boil'.

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