Continuous Time-Dependent Measurements: Quantum Anti-Zeno Paradox with Applications

Abstract

We derive differential equations for the modified Feynman propagator and for the density operator describing time-dependent measurements or histories continuous in time. We obtain an exact series solution and discuss its applications. Suppose the system is initially in a state with density operator $\rho (0)$ and the projection operator $E(t)=U(t)E{U}^{†}(t)$ is measured continuously from $t=0$ to $T$, where $E$ is a projector obeying $E\rho (0)E=\rho (0)$ 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 $E(T)\ne E$ and the watched system is sure to change its state, which is the anti-Zeno paradox noted by us recently. Our results valid for projectors of arbitrary rank generalize those obtained by Anandan and Aharonov for projectors of unit rank.

16 pages, latex; new material and references added

References in corpus (1)

• A Quantum Anti-Zeno Paradox

Cited by in corpus (1)

• Entropy of the Information Retrieved from Black Holes