Zeno Dynamics, Indistinguishability of State, and Entanglement

According to the quantum Zeno effect (QZ), frequent observations of a system can dramatically slow down its dynamical evolution. We show that the QZ is a physical consequence of the statistical indistinguishability of neighboring quantum states. The time scale of the problem is expressed in terms of the Fisher information and we demonstrate that the Zeno dynamics of particle entangled states might require quite smaller measurement intervals than classically correlated states. We propose an interferometric experiment to test the prediction.

Figure 1

Two different setups consisting of a sequence of $m$ Mach-Zehnder interferometers. The phase shift in each MZ interferometer is $\theta /m$. The input state is the product $|{\psi }_a⟩|{\psi }_b⟩$. (a) The MZ interferometers are sequentially connected so that the output of each interferometer becomes the input of the next one. (b) Only one output port becomes the input of the next interferometer. The second output port remains disconnected, while the corresponding input port of the next MZ interferometer is injected with $|{\psi }_a⟩$.

Figure 2

Energy level diagram of the experiment [8]. A resonant radio-frequency magnetic field couples the $a$ and $b$ modes. A sequence of $m$ laser pulses resonantly couples the levels $a$ and $c$. The ions in the level $c$ decay only in the level $a$ with induced fluorescence proportional to the number of particles populating the mode $a$.