Continuous Time-dependent Measurements: Quantum Anti-zeno Paradox with Applications
نویسنده
چکیده
We derive a differential equation for the modified Feynman propagator describing timedependent measurements or histories continuous in time. We obtain an exact series solution and its applications. Suppose the system is initially in a state with density operator ρ(0) and the projection operator E(t) = U(t)EU (t) is measured continuously from t = 0 to T , where E is a projector obeying Eρ(0)E = ρ(0) and U(t) a unitary operator obeying U(0) = 1 and some smoothness conditions in t. Then the probability of always finding E(t) = 1 from t = 0 to T is unity. Generically E(T ) 6= E and the watched system is sure to change its state, which is an anti-Zeno paradox. For history-extended closed quantum systems, the weight of the history E(t) = 1 from t = 0 to T is unity.
منابع مشابه
A Quantum Anti-zeno Paradox
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)EU (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 ...
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