Experimental demonstration of the quantum Zeno effect in NMR with entanglement-based measurements

We experimentally demonstrate a dynamic fashion of quantum Zeno effect in nuclear magnetic resonance systems. The frequent measurements are implemented through quantum entanglement between the target qubit(s) and the measuring qubit, which dynamically results from the unitary evolution of duration ${\tau }_m$ due to dispersive coupling. Experimental results testify to the presence of “the critical measurement time effect,” that is, the quantum Zeno effect does not occur when ${\tau }_m$ takes some critical values, even if the measurements are frequent enough. Moreover, we provide an experimental demonstration of an entanglement preservation mechanism based on such a dynamic quantum Zeno effect.

Figure 1

(a) General dynamic approach for QZE and (b) the corresponding schematic diagram for experiments. Frequent measurements $M$ are driven by the interaction Hamiltonian $H_M$, while the free evolution $U$ of the system is implemented by rf pulses applied on the system. In the end, we read out the information about the system just from the apparatus via the QND measurement. The free-evolution $U$ process is neglected during the strong measurement $M$ process.

Figure 2

Pulse sequences for observing entanglement-based QZE: in a single-qubit system (a), and in a composite system for a product state $|00\rangle$ (b), and for a pseudoentangled state $|{\varphi }^{+}\rangle$ (c). Each $M$ process lasts about $2.5\sim 3.0$ ms for the single-qubit system and about $28\sim 33$ ms for the composite system. Here, $\theta =5^{\circ }\sim 6^{\circ }$, $\eta =400\pi {\tau }_m$, $d_1=\frac{100{\tau }_m}{2|J_{12}|}$, $d_2=\frac{250{\tau }_m}{2|J_{01}|}$, and $d_3=\frac{250{\tau }_m}{2|J_{02}|}$.

Figure 3

Experimental QZE with entanglement-based measurement on single-qubit system. (a) Experimental observations of QZE with a series of rf pulses and measurements (left side) and with GRAPE engineering (right side). The amplitude decay in the left panel is simulated by adding an exponential decay $\exp (-k{\tau }_m)$ to each $M$ process ($k=1.25$, $0.8,$ and $0.7$, respectively, for ${\tau }_m=2.517,2.55$, and 3 ms). (b) Evolution paths of the system on the Bloch sphere, corresponding to the three experiments with the measurement times ${\tau }_m=2.517,2.550,\text{and}3.000$ ms.

Figure 4

(a) Experimental QZE with entanglement-based measurement on two-qubit system for a product state (top plots) and (b) an entangled state (bottom plots). (b) Real part of the reconstructed density matrix of the initial and final states for preserving the entangled state via QZE.